Question

Here's a graph of a linear function. Write the equation that describes that function. (Express it in slope-intercept form.)

Answer 1

Answer:

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

Step-by-step explanation:

The equation of a linear function in a slope-intercept form is written as

$y=mx+q$

where

m is the slope of the line

q is the y-intercept

We proceed as follows. First of all, we find the y-intercept, which is the value of y at which the line touches the y-axis.

From the graph, we see that this occurs at y = 4, therefore the y-intercept is

$q=4$

Now we have to find the slope. We do that by choosing two points along the line, with coordinates $(x_1,y_1)$ and $(x_2,y_2)$ and by using the equation

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

Here we take the two points:

(0,4)

(-8,0)

So the slope is

$m=\frac{4-0}{0-(-8)}=\frac{1}{2}$

Therefore, the equation of the line is

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