1

Problem

A linear function f(x) has a slope of 4 and passes through the point (4, 8). Find the equation of the linear function.

2

Step

Given values are

f(x) = 4 and point (4,8)

3

Formula

To find the equation of the linear function, we can use the point-slope form of a linear equation: \$y - y_1 = m(x - x_1)\$.

4

Step

where \$(x_1, y_1)\$ is the given point on the line, and m is the slope:

\$x_1 = 4 and y_1 = 8\$ and m = 4

5

Step

Substitute the value in the formula then we get the equation:

y - 8 = 4(x - 4)

y - 8 = 4x - 16

y = 4x - 8

6

Solution

Therefore, the equation of the linear function is f(x) = 4x - 8.

7

Sumup

Please summarize steps

Choices

8

Choice-A

This option suggests a y-intercept of -9, which is incorrect; the y-intercept should be -8

Wrong f(x) = 4x - 9

9

Choice-B

This option suggests a positive y-intercept of +8, which is incorrect; the y-intercept should be negative

Wrong f(x) = 4x + 8

10

Choice-C

This option also suggests a positive y-intercept of +9, which is incorrect; the y-intercept should be negative

Wrong f(x) = 4x + 9

11

Choice-D

This option suggests a correct y-intercept of -8, which matches the solution we derived, making it the correct option

Correct f(x) = 4x - 8

12

Answer

Option

D

13

Sumup

Please summarize choices