Question

Find the equation of the linear function represented by the table below in slope-intercept form. x: 1 2 3 4 y: -2 -5 -8 -11

Answer 1

y = -3x + 1

Answer 2

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

First, we can find the slope by using the formula:
slope = (change in y) / (change in x)

From the table, we can see that when x increases by 1, y decreases by 3. Therefore, the change in y is -3 and the change in x is 1.

Slope = (-3) / (1) = -3

Next, we can substitute the slope into the slope-intercept form of a linear equation, y = mx + b, where m is the slope:

y = -3x + b

To find the y-intercept (b), we can choose any point from the table. Let's use the point (1, -2).
Substituting these values into the equation, we get:

-2 = -3(1) + b

Solving for b:
-2 = -3 + b
b = -2 + 3
b = 1

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

y = -3x + 1.