Find the equation of the linear function represented by the table below in slope-intercept form. x: -2 1 4 7 y: -1 -7 -13 -19

Answer 1

To find the equation of the linear function in slope-intercept form, we need to determine the slope and y-intercept.

First, let's find the slope (m) using the formula:

m = (change in y) / (change in x)

We can choose any two points from the table to calculate the slope. Let's use the points (-2, -1) and (1, -7).

m = (-7 - (-1)) / (1 - (-2))
m = (-7 + 1) / (1 + 2)
m = -6 / 3
m = -2

Next, we can substitute the slope (m) into the slope-intercept form of a linear equation, which is y = mx + b, to find the y-intercept (b).

Using the coordinates of one point (-2, -1):

-1 = -2(-2) + b
-1 = 4 + b
b = -1 - 4
b = -5

Therefore, the equation of the linear function represented by the table in slope-intercept form is:

y = -2x - 5