Question

What is the answer to x 3,6,9,12 y -6,-12,-18,-24 y=mx+b

Answer 1

The equation of the line or linear function is:

y = -2x

Explanation:

Given the table

x 3 6 9 12

y -6 -12 -18 -24

As there is a constant change in x and y values, so the table represents the linear function.

The slope-intercept form of the linear equation

y = mx+b

where

• m is the slope

• b is the y-intercept

Taking any two points, let say

• (3, -6)

• (6, -12)

Determining the slope between (3, -6) and (6, -12)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`m=(-12-\left(-6\right))/(6-3)`

Refine

`m=-2`

Thus, the slope m = -2

now substituting m = -2 and (3, -6) in the slope-intercept form

y = mx+b

-6 = -2(3) +b

-6 = -6 + b

b = -6 + 6

b = 0

Thus, the y-intercept b = 0

now substituting m = -2 and b = 0 in the slope-intercept form of linear function

y = mx+b

y = -2x + 0

y = -2x

Therefore, the equation of line or linear function is:

y = -2x