Question

Find the equation of the linear function represented by the table below in slope-intercept form. XY-153-117-2711-43

Answer 1

First, we have to find the slope, using the following formula.

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's use the points (-1,5) and (7, -27). Where,

$\begin{gathered} x_1=-1 \\ x_2=7 \\ y_1=5 \\ y_2=-27 \end{gathered}$

Then, we use these values to find the slope.

$m=\frac{-27-5}{7-(-1)}=\frac{-32}{8}=-4$

Now we use the point-slope formula.

$\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-4(x-(-1)) \\ y-5=-4(x+1) \\ y-5=-4x-4 \\ y=-4x-4+5_{} \\ y=-4x+1 \end{gathered}$

Therefore, the slope-intercept form is y = -4x+1.