The equation y = mx + 6 defines what type of function? (1 point)

Question

• an initial value function
• a nonlinear function
• а linear function
• a slope function

Answer 1

a linear function

Answer 2

Use the table to answer the question.
x y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y = mx + 6 form.
(1 point)

Answer 3

To find the equation of the linear function, we first need to find the slope (m).

Using the points (6, 16) and (15, 43) from the table:

m = (y2 - y1) / (x2 - x1)
m = (43 - 16) / (15 - 6)
m = 27 / 9
m = 3

Now that we have the slope, we can use one of the points to find the y-intercept (b).

Using the point (6, 16):
16 = 3(6) + b
16 = 18 + b
b = -2

Therefore, the equation of the linear function is:
y = 3x - 2

Answer 4

Use the table to answer the question.
У
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y = mx + b form.
(1 point)

Answer 5

Given the points (6, 16) and (15, 43), we can determine the equation of the linear function using the slope-intercept form (y = mx + b).

First, calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (43 - 16) / (15 - 6)
m = 27 / 9
m = 3

Now that we have the slope, we can use one of the points to find the y-intercept (b).

Using the point (6, 16):
y = mx + b
16 = 3(6) + b
16 = 18 + b
b = 16 - 18
b = -2

Therefore, the equation of the linear function in slope-intercept form is:
y = 3x - 2

Answer 6

Use the table to answer the question.
x y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y = mx + b form.
(1 point)

Answer 7

Given the points (6, 16) and (15, 43), we can determine the equation of the linear function using the point-slope form (y - y1 = m(x - x1)) or the slope-intercept form (y = mx + b).

First, calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (43 - 16) / (15 - 6)
m = 27 / 9
m = 3

Now, choose one of the points to substitute into the point-slope form.
Using the point (6, 16):
y - 16 = 3(x - 6)
y - 16 = 3x - 18
y = 3x - 2

Therefore, the equation of the linear function in y = mx + b form is:
y = 3x - 2

Answer 8

Last year, Alayah ordered 4 cubic yards of soil and spent $220. This year, she orders 7 cubic yards of soil and spends $340. Write the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost.
Enter your answer in y = mx + b form. (1 point)

Answer 9

To find the equation of the linear function that models the relationship between the number of cubic yards of soil ordered (x) and the total cost (y), we need to determine the slope and the y-intercept.

First, let's find the slope (m) using the given points:
m = (change in y) / (change in x)
m = (340 - 220) / (7 - 4)
m = 120 / 3
m = 40

Now, we can find the y-intercept (b) by substituting the slope and one of the points (e.g., (4, 220)) into the equation y = mx + b:
220 = 40(4) + b
220 = 160 + b
b = 220 - 160
b = 60

Therefore, the equation of the linear function in y = mx + b form is:
y = 40x + 60

Answer 10

Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change? Choose 1 for Linear Function 1;
choose 2 for Linear Function 2.
• Linear Function 1: y = × + 8
• Linear Function 2: Points (2,6) and (4,10)

Answer 11

Linear Function 1 has the equation y = x + 8, so the slope (rate of change) is 1.

For Linear Function 2, we need to calculate the slope using the given points (2,6) and (4,10):
slope (m) = (y2 - y1) / (x2 - x1)
slope (m) = (10 - 6) / (4 - 2)
slope (m) = 4 / 2
slope (m) = 2

Therefore, Linear Function 2 has a greater rate of change (slope) compared to Linear Function 1. Choose 2 for Linear Function 2.