Question

Here's a graph of a linear function. Write the equation that describes that function.

(Express it in slope-intercept form.)

Answer 1

The slope-intercept form of the graph is $y=\frac{1}{2} x+4$.

Solution:

Let us take any point on the straight line.

Here, we take (–8, 0) and (0, 4).

Let us first find the slope of the line.

Slope of the line formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$x_1=-8, y_1=0, x_2=0, y_2=4$

$m=\frac{4-0}{0-(-8)}$

$m=\frac{4}{8}$

$m=\frac{1}{2}$

Slope-intercept form:

$y-y_1=m(x-x_1)$

$y-0=\frac{1}{2} (x-(-8))$

$y=\frac{1}{2} (x+8)$

$y=\frac{1}{2} x+\frac{8}{2}$

$y=\frac{1}{2} x+4$

Hence the slope-intercept form of the graph is $y=\frac{1}{2} x+4$.