Answer:
$6555
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
i thought of a number, multiplied it by 2 1 2 , divided the result by 1 1 5 , subtracted 7 18 from it, and got 1 5 6 . what was my number?
To determine the number you thought of, let's work backward from the given result of 156. We determined that the number you thought of was 490.
By following the steps in reverse order, we can calculate the original number. We start with the given result of 156. To reverse the subtraction, we add 7 18 to it, which gives us 8 7 4. Moving further, to reverse the division, we multiply 8 7 4 by 1 1 5, resulting in 1 0 0 5 6 0. Now, to reverse the multiplication, we divide 1 0 0 5 6 0 by 2 1 2, yielding 4 9 0. Hence, the number you initially thought of was 4 9 0.
In summary, by working backward from the given result of 156, we determined that the number you thought of was 490.
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Calculate following areas and show all steps for complete marks: 1) Limited by the function y=x2, the x-axis and the points x=−2 and x=2 (5 points) 2) Limited by the function y=2xex2, the x-axis and the points x=0 and x=3 (20 points) 3) Limited by the function y=x2−3x4x−6 the x-axis and the points x=−1 and x=4.(20 points) 4) Limited by the function y=sin3x, the x-axis and the points x=10 and x=20, where 10 and 20 are degrees. (15 points) 5) Limited by the function y=xex, the x-axis and the points x=1 and x=2 (10 points) 6) Limited by the function y=xe2x, the x-axis and the points x=2 and x=3 (10 points) 7) Limited by the function y=x4−8x2+10x−4 the x-axis and the points x=1 and x=2.
The given function is y = x⁴ − 8x² + 10x − 4. The x-axis is included from 1 to 2. Here, we need to divide the function at the point of intersection with the x-axis to simplify the integral.Hence, these are the required solutions of the given question
Here is the solution to the provided problem:
1. The given function is y = x². The x-axis is included from -2 to 2.
Here, the curve intersects the x-axis at x = 0, hence, we need to divide the curve at x = 0 to simplify the integral. Therefore, the required area is:
2. The given function is y = 2xe^(x^2).
The x-axis is included from 0 to 3.
Here, we need to use integration by substitution to find the area.
3. The given function is y = x² − (3x/4) − (6/4x).
The x-axis is included from -1 to 4.
Here, we need to divide the function at the point of intersection with the x-axis to simplify the integral.
4. The given function is y = sin3x.
The x-axis is included from 10 to 20 degrees.
Here, we need to use integration by substitution to find the area.
5. The given function is y = xe^x.
The x-axis is included from 1 to 2.
Here, we need to use integration by parts to find the area.
6. The given function is y = xe^(2x).
The x-axis is included from 2 to 3.
Here, we need to use integration by parts to find the area.
7. The given function is y = x⁴ − 8x² + 10x − 4.
The x-axis is included from 1 to 2.
Here, we need to divide the function at the point of intersection with the x-axis to simplify the integral.
Hence, these are the required solutions of the given question.
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can you please try doing question 9 and 10? (explain also in a short or long way) thank you
Thus, the correct statement is B: The speed of Becca's car is more.
Explain about the rate of change:An indicator of how 1 quantity changes in proportion to another is called a rate of change. Positive or negative change rates are possible. This is equivalent to a change in the y-value in between two data points. Zero rate of change refers to a quantity that does not fluctuate over time.
Relation between speed and time:
speed = distance/ time
Tom's car:
distance d = 120 miles
Time t = 3 hours
speed of Tom's car = 120/3 = 40 miles/hours
Becca's car:
distance d = 90 miles
Time t = 2 hours
speed of Becca's car = 90/2 = 45 miles/hours
Thus, the correct statement is B: The speed of Becca's car is more.
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Correct questions:
The correct question is given by question 9.
Please help‼️ domain and range‼️
The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively
Calculating the domain and range of the graph?From the question, we have the following parameters that can be used in our computation:
The graph
The above graph is an exponential function
The rule of an function is that
The domain is the set of all real values
In this case, the domain is (-∝, ∝)
For the range, we have
Range = (0, ∝)
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Consider a perfectly shuffled 52-card deck dealt to 4 players. Find the probability that one player (any one of the four players) gets all aces.
The probability that one player gets all aces is 0.0467
Finding the probability that one player gets all aces.From the question, we have the following parameters that can be used in our computation:
Cards, n = 52
Players, r = 4
The 52 cards can be shared to the the 4 players in C(n + r - 1, r - 1) ways
So, we have
C(52 + 4 - 1, 4 - 1) = C(55, 3)
When evaluated, we have
C(52 + 4 - 1, 4 - 1) = 26235
Next:
The remaining 48 cards can be shared to the other 3 players in C(n + r - 1, r - 1) ways
C(48 + 3 - 1, 3 - 1) = C(50, 2)
C(48 + 3 - 1, 3 - 1) = 1225
So, we have
P = 1225/26235
Evaluate
P = 0.0467
Hence, the probability is 0.0467
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Data are weight changes of humans, tabulated after administration of a drug proposed to result in weight loss Each weight change (in kg) is the weight after minus the weight before drug administration. A random sample of 12 subjects was selected to participate in this research. Which formulas should be used if the researcher wishes to make confidence intervals and do hypothesis testing? i. Type of problem: ii. What other information would you need to know to check the assumptions you need for this test?
The researcher can use certain formulas for finding confidence intervals and hypothesis testing in this scenario.
For confidence intervals, the formula for the mean difference would be used, which is the average of the weight changes in the sample.
This formula calculates the range within which the true population mean difference is likely to fall.
To conduct hypothesis testing, the researcher can use the formula for the t-test for a single sample.
This test compares the mean difference observed in the sample to a hypothesized value and determines whether there is enough evidence to support or reject the hypothesis.
To check the assumptions necessary for this test, the researcher would need additional information. The assumptions typically include:
1. Random sampling: It is important to ensure that the subjects were randomly selected from the population to generalize the results.
2. Normality: The weight changes should follow a normal distribution within the population.
The researcher would need to assess the normality assumption, such as by examining the distribution of weight changes or using statistical tests like the Shapiro-Wilk test.
3. Independence: The weight changes of one subject should not be influenced by the weight changes of another subject.
This assumption can be violated if the subjects are related or if there are repeated measurements on the same subjects.
By checking these assumptions and using the appropriate formulas, the researcher can make confidence intervals and perform hypothesis testing to draw conclusions about the effects of the drug on weight loss in the population.
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please help factorise 7ab+a
Answer:
= a(7b + 1)
Step-by-step explanation:
7ab + a
a(7b + 1).
What is a point-slope equation of the line with slope - 10 that goes through the point (1.4) Ay- 4 = -10(x - 1) By+43-10(x+1) O c. y - 4 = 10(x-1) D. + 4 = 10(x+1)
Answer:
y-4=-10(x-1)
Step-by-step explanation:
A point-slope equation of the line with the given slope and coordinate point is (y-4)=-10(x-1).
What is the point slope form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The equation of the point slope form is: (y - y₁) = m(x - x₁)
where, (x, y) is a random point on the line and m is the slope of the line.
Given that, slope (m)=-10 and (x₁, y₁)=(1, 4).
Substitute m=-10 and (x₁, y₁)=(1, 4) in (y - y₁) = m(x - x₁), we get
(y-4)=-10(x-1)
Therefore, a point-slope equation of the line with the given slope and coordinate point is (y-4)=-10(x-1).
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I’ll give brainliest! Please explain in your words why you think 180 degrees and n-2 are in the Polygon Angle- Sum Formula, 180 degrees (n-2) ?!
Answer:
If you look back at the formula, you'll see that n – 2 gives the number of triangles in the polygon, and that number is multiplied by 180, the sum of the measures of all the interior angles in a triangle. Do you see where the "n – 2" comes from? It gives us the number of triangles in the polygon.
Have a nice day :)
What will be the sales price of the car if it has a regular price of $16000 and is on sale for 20% off? Determine the cost of the car including 13% tax.
Answer:
Total cost = $14464
Step-by-step explanation:
Step 1: Multiply the discount percentage by the regular price to determine the discount amount:
0.20 * 16000 = 3200
Thus, the 20% discount lowers the regular price by $3200.
Step 2: Subtract the discount amount from the regular price to determine the new price:
16000 - 3200 = 12800.
Thus, the subtotal is $12800
Step 3: Multiply tax percentage by subtotal to determine tax:
0.13 * 12800 = 1664
Thus, the 13% tax rate would raise the subtotal by $1664.
Step 4: Add the tax to the subtotal to find the cost price.
1664 + 12800 = 14464.
Thus, the total cost of the car is $14464.
Thus, the total cost of the car with the 20% discount and the 13% tax is 14464.
For each function f(n):Z
+
→R
+
give the value of smallest integer k such that f(n)∈O(n
k
). In other words, give the value of k such that O(n
k
) is the most restrictive polynomial-time upper bound of f(n). If no such bound exists, type 8 e99 in the space provided. A) 3n
2
+
n
1
∈O(n
k
)k= B) 17
3
n+4
+5
7n
+4∈0(n
k
)k= C) 2
lgn
+1000000∈O(n
k
)k= D) 3
2n+1
∈O(n
k
)k= E) 5n
2
lg
n
3
+4n+7
∈O(n
k
)k=
A) k = 2 B) k = 8 C) k = 8 D) k = 1 E) k = 2. In cases where no polynomial-time upper bound exists, the value of k is represented as 8e99, indicating an extremely large value.
A) The function f(n) = 3n^2 + n has a polynomial-time upper bound of O(n^2). Therefore, the smallest integer k such that f(n) ∈ O(n^k) is k = 2.
B) The function f(n) = 17^(3/n) + (4/7n)^5 has no polynomial-time upper bound. Hence, the value of k is 8e99.
C) The function f(n) = 2log(n) + 1000000 has no polynomial-time upper bound. Thus, the value of k is 8e99.
D) The function f(n) = 3^(2n+1) has a polynomial-time upper bound of O(n^1). Therefore, the smallest integer k such that f(n) ∈ O(n^k) is k = 1.
E) The function f(n) = 5n^2 log(n^3) + 4n + 7 has a polynomial-time upper bound of O(n^2). Thus, the smallest integer k such that f(n) ∈ O(n^k) is k = 2.
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Solve the equation for x: 212 = 314x.
Answer:
x=106/157
Step-by-step explanation:
Answer:
x=10/13
Step-by-step explanation:
A rectangular room is
4
meters longer than it is wide, and its perimeter is
32
meters. Find the dimension of the room.
Find the length and the width.
Answer: 60 m squared dimensions
6 m width
10 m length
Step-by-step explanation:
subtract 8 from the perimeter to account for 2 sides having the extra length then divide the answer by 4 to get the length if all the sides were equal
32-8=24
24/4=6
then add the 4 m back to the answer to get the length
Sara used a number line to add. She started counting at 10, and then she counted until she
was over the number -4 on the number line. If Sara is modeling addition, what number did
she have to add to 10?
Answer:
-14
Step-by-step explanation:
A new Youth Sports Center is being built in Hadleyville, The perimeter of the rectangular playing field is 430 yards. The length of the field is 5 yards
the width. What are the dimensions of the playing field?
The width is
yards
The length is
yards
Answer:
Width = 44 yards
Length = 171 yards
Step-by-step explanation:
given data
length of the field = 5 yards
Perimeter of the rectangular field = 430 yards.
solution
we consider here length of the field = L
and width of the field = W
as we know length of the field 5yards less than quadruple the width
so here
L = 4W - 5 .....................................1
and
Perimeter (P) will be here
P = 2(L + W) ............................................2
put here equation 1 value
430 = 2(4W - 5 + W)
solve it we get
W = 44
so here put value in eq 1 we het
L = 4W - 5
L = 4(44) - 5
L = 171
so, length of the field is 171 yards
A sample was taken of dogs at a local dog park on two random days. The counts are displayed on the unit below. if there are an estimated of 50 dogs at the dog park at any given time, which proportion could be used to find the average number of shepherd mixes at any given time?
sample 1
Labrador Retriever 4
Shepherd Mix 7
Chihuahua 3
Poodle 1
Australian Cattle Dog 2
sample 2
Labrador Retriever 5
Shepherd Mix 9
Chihuahua 5
Poodle 2
Australian Cattle Dog 4
1. 8/21 = x/50
2. 16/21 = x/50
3. 8/50 = x/42
4. 7/9 = x/50
The proportion that could be used to find the average number of shepherd mixes at any given time is given as follows:
4. 7/9 = x/50
How to obtain the proportion?The proportion is obtained as the ratio between two amounts, dividing the amount a by the amount b.
The number of Sheperd Mix in each sample is given as follows:
7 and 9.
Hence the first part of the ratio is of 50, hence:
7/9.
As the total number is of 50, the second part is given as follows:
x/50.
Hence the proportional equation is given as follows:
7/9 = x/50.
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y=mx+b The fit parameters obtained from the reqression are the slope ( m ) and y-intercept (b). In EXCEL the data was analyzed using the LINEST formula 5 2. An unknown was measured and gave a signal of 80.77. Determine the concentration for the analyte in the unknown using the fit parameters and the linear model. 4.0□[]ppmCo 2+
To determine the concentration of the analyte in the unknown using the fit parameters and the linear model, you need to substitute the given signal value into the equation y = mx + b.
In this case, the linear model is represented by the equation y = mx + b, where:
y is the signal value (80.77 in this case),
m is the slope obtained from the regression analysis, and
b is the y-intercept obtained from the regression analysis.
You haven't provided the values of m and b, so I'll use placeholders for now.
Let's assume the slope (m) obtained from the LINEST formula is m = 2.5 and the y-intercept (b) is b = 10.
Substituting these values into the equation:
y = mx + b
80.77 = 2.5x + 10
To find the concentration (x), we can rearrange the equation:
2.5x = 80.77 - 10
2.5x = 70.77
x = 70.77 / 2.5
x ≈ 28.31
Therefore, based on the given fit parameters and the linear model, the concentration of the analyte in the unknown is approximately 28.31 ppm Co2+.
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Which table of values represents the exponential function f(x)=0.1x−4?
Answer:
for the 1 one is: ___________Find the x and y Intercepts___________
for the 2 one it is a: ________Graph_________
Step-by-step explanation:
BRAINLYLIST will highly appreciated
HAVE A GOD LIKE DAY
Determine whether the lines are parallel or perpendicular. Explain your answer
2y = 16+ 42
бу — 30 = 12х
Answer:
Neither
Step-by-step explanation:
2y = 16x + 42
y = 8x + 21
Slope=8
6y - 30 = 12x
6y = 12x + 30
y = 2x + 5
Slope=2
Help me ASAP please!!!
Answer:
85 inches²
Step-by-step explanation:
Each triangle equals 15 inches
15(4)=60
Square= 5×5=25
60+25=85 inches²
100 POINTS AND BRAINLIEST TO WHOEVER SOLVES IT
The edge length, s, of a regular tetrahedron is approximately given by , where V is the volume of the terahedron. Use a graphing calculator to graph the function. Estimate the volume of a regular tetrhedron with an edge length of 4 inches.
Volume of a tetrahedron with edge s
\(\\ \rm\Rrightarrow V=\dfrac{s^3}{6\sqrt{2}}\)
According to question
s=4in\(\\ \rm\Rrightarrow V=\dfrac{4^3}{6\sqrt{2}}\)
\(\\ \rm\Rrightarrow V=\dfrac{64}{6\sqrt{2}}\)
\(\\ \rm\Rrightarrow V=\dfrac{32}{3\sqrt{2}}\)
\(\\ \rm\Rrightarrow V=\dfrac{32}{4.2426406871192}\)
\(\\ \rm\Rrightarrow V\approx 7.5425in^3\)
Answer:
See below ~
Step-by-step explanation:
Volume of a tetrahedon
V = s³ / 6√2s = edge lengthSolving for V
V = (4)³ / 6√2V = 64 / 6√2V = 32 / 3√2V = 32√2 / 6V = 16√2 / 3V = 7.54 cubic inchesGraph
In Exercises 1-4, W is a subspace of the vector space V of all (2 x 2) matrices. A matrix A in W is written as Ir a b --[:] A р ir с d 1 In each case exhibit a basis for W. 1. W= = {A: a +b+c+d=0} 2. W = {A: a = -d, b = 2d, c= -3d} 3. W = {A: a =0} 4. W = {A: b = a - c, d = 2a +c} AAA
Both A1 and A2 belong to W, and they are linearly independent, so they form a basis for W.
1. To find a basis for W = {A: a + b + c + d = 0}, we can start by writing a general matrix in W as:
A =
[ r a b ]
[ c -r -a ]
where r is a free parameter. Then we can rewrite the condition a + b + c + d = 0 as:
a = -b - c - d
Substituting this into the matrix A, we get:
A =
[ r -b -c -d ]
[ c -r b c ]
Now we can see that the matrix A has two free parameters (r and d), and the remaining entries are determined by b and c. We can choose b = 1 and c = 0 to get:
A1 =
[ r -1 0 -r ]
[ 0 -r 1 0 ]
and we can choose b = 0 and c = 1 to get:
A2 =
[ r 0 -1 r ]
[ 1 -r 0 0 ]
Both A1 and A2 belong to W, and they are linearly independent, so they form a basis for W.
2. To find a basis for W = {A: a = -d, b = 2d, c = -3d}, we can write a general matrix in W as:
A =
[ r 2d -3d ]
[-d -r d ]
where r is a free parameter. Then we can see that the matrix A has one free parameter (d), and the remaining entries are determined by r. We can choose d = 1 to get:
A1 =
[ r 2 -3 ]
[-1 -r 1 ]
and we can choose d = 0 to get:
A2 =
[ r 0 0 ]
[ 0 -r 0 ]
Both A1 and A2 belong to W, and they are linearly independent, so they form a basis for W.
3. To find a basis for W = {A: a = 0}, we can write a general matrix in W as:
A =
[ 0 b ]
[ c d ]
where b, c, and d are free parameters. Then we can see that the matrix A has two free parameters (b and d), and the remaining entries are determined by c. We can choose b = 1 and d = 0 to get:
A1 =
[ 0 1 ]
[ c 0 ]
and we can choose b = 0 and d = 1 to get:
A2 =
[ 0 0 ]
[ c 1 ]
Both A1 and A2 belong to W, and they are linearly independent, so they form a basis for W.
4. To find a basis for W = {A: b = a - c, d = 2a + c}, we can write a general matrix in W as:
A =
[ a a - c ]
[ c 2a + c ]
where a and c are free parameters. Then we can see that the matrix A has two free parameters (a and c), and the remaining entries are determined by these parameters. We can choose a = 1 and c = 0 to get:
A1 =
[ 1 1 ]
[ 0 2 ]
and we can choose a = 0 and c = 1 to get:
A2 =
[ 0 -1 ]
[ 1 1 ]
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Compare and Contrast: Below are two expressions. Simplify each and then choose the statement that is true.
Expression #1
Expression #2
(3d)3(d)
(3d2)2
Answer:
Below are two expressions. Simplify each and then choose the statement that is true. Expression #1 Expression #2 (3d)3(d) (3d2)2 The exponents in Expression #1 are greater than the exponents of Expression #2. The exponents on Expression #2 are greater than the exponents of Expression #1. The exponents of Expression #1 are the same as the exponents of Expression #2. The relationship cannot be determined with the given information.
If there are 5 green, 6 yellow, 8 blue, and 7 brown M&M's, what is the probability that you choose a blue?
Answer:
the probability is 69/420
Answer:
4/13.
Step-by-step explanation:
The probability is the number of blue M&M's over the total.
The total is 5+6+8+7=26.
There are 8 blue M&M's.
8/26=4/13
Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. the first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.
1. Write an equation for each tank representing the total amount of water in gallons in the tank, y, in terms of the number of hours, x, that the tank drains
2. what is the solution to this system of equations.
3. suppose Aiko starts draining the tanks at the same time. When will both tanks have the same amount of water? How much water is in each tank at that time
The answers to each part is mentioned above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.
( 1 ) -Equation for tank {1} -
y = 175 - 25x
Equation for tank {2} -
y = 200 - 30x
( 2 ) -For the solution we can write -
175 - 25x = 200 - 30x
- 25x + 30x = 200 - 175
5x = 25
x = 5
and
y = 200 - 150
y = 50
( 3 ) -For the same amount of water we can write -
175 - 25x = 200 - 30x
- 25x + 30x = 200 - 175
5x = 25
x = 5 hours
In tank (1), there is : 175 - 25 x 5 = 50 gallons
In tank (2), there is : 200 - 30 x 5 = 50 gallons
Therefore, the answers to each part is mentioned above.
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Are the equations 1/2x-8=9 and x-8=18 equivalent?
Answer:
not equivalent
Step-by-step explanation:
solve for x to see if they are equivalent
1/2x-8=9 and x-8=18
1/2x=17
x=34
x-8=18
x = 36
no they are not equivalent
A plumber gave an estimate for the renovation of a kitchen. Her hourly rate is $55 per hour and the parts for the renovation will cost $234.
If her total estimate is $509.00, how long does she expect the job to take?
hours
a.6 hours
b.7 hours
c.4 hours
d.5 hours
Answer:
12 houra
Step-by-step explanation:
404-80=27x
324=27x
x=324/27
x=12 hours.
The job is expected to take 5 hours, Option d.
What is unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
According to the given problem,
Cost for parts = $234
Total estimate = $509.00
Amount left from total estimate after spending for parts = $( 509 - 234 )
= $275
Hourly rate for renovation = $55
Total hours = \(\frac{275}{55}\) hours
= 5 hours.
Hence, we can conclude that she with $275, 5 hours of job can be afforded.
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Two different linear functions are shown below with two points given from each function. Use slope-intercept form or point-slope form to find the equation of each.
Linear Function A
Points: (–5, –2), (–5, 7)
Linear Function B
Points: (7, –5), (–2, –5)
Function A has
✔ no slope
.
The equation of line A is
✔ x = -5
.
Function B has
✔ a slope of 0
.
The equation of line B is
✔ y = -5
.
here are the answersss
Answer:
Function A has
✔ no slope
.
The equation of line A is
✔ x = -5
.
Function B has
✔ a slope of 0
.
The equation of line B is y= -5
Step-by-step explanation:
i did the online assighnment
The true expressions about functions A and B from the options given are :
Function A has no slope Function B has a slope of 0Equation of line B is y = - 5Function A :
Points: (–5, –2), (–5, 7)
Slope = (7 - (-2)) ÷ (-5 - (-5)) = 9 ÷ 0 = 0
From :
y = bx + c b = slope ; c = interceptWe can obtain c, thus ;
-2 = 0(-5) + c
-2 = c
y = - 2
Function B :
Points:(7, –5), (–2, –5)
Slope = (-5 - (-5)) ÷ (-2 - 7) = 0 ÷ - 9= 0
From :
y = bx + cb = slope ; c = intercept
We can obtain c, thus ;
-5 = 0(7) + c
-5 = c
y = -5
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What is the equation of this graphed line?
Answer:
y=1/3x-5
Step-by-step explanation:
y=mx+b
Y=slope x+y-intercept
slope 2/6 = 1/3
y-int= -5
equation of the line that passes through the points (7, 6) and (-2, -3)?
Answer:
y=x-1
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the points (7, 6) and (-2, -3)
There are 3 ways to write the equation of the line:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept Point-slope form, which is \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a pointStandard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negativeThe most common (and usually, the easiest way) would be slope-intercept form, so let's write it that way
First, we'll need to find the slope of the line
The slope can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points
We have two points, which is needed, but let's label their values in order to avoid any confusion:
\(x_1= 7\\y_1=6\\x_2=-2\\y_2=-3\)
Now substitute these values into the formula to find the slope (m):
m=\(\frac{y_2-y_1}{x_2-x_1}\)
m=\(\frac{-3-6}{-2-7}\)
Subtract the numbers
m=\(\frac{-9}{-9}\)
Divide
m=1
The slope of the line is 1
So far, we can write the equation of the line as this:
y=1x+b, or y=x+b
We'll need to find b
As the equation passes through both (7,6) and (-2, -3), we can use either one of them to solve for b
Taking (7, 6) for instance, substitute 7 as x and 6 as y:
6=1(7)+b
Multiply
6=7+b
Subtract 7 from both sides
-1=b
Now substitute -1 as b:
y=x-1
Hope this helps!