Answer:
[tex]y=-\frac{1}{4} x-6[/tex]
Step-by-step explanation:
The slope-intercept form is [tex]y=mx+c[/tex], where m is the slope of the line and c is where the line crosses the [tex]y[/tex]-axis.
To calculate [tex]m[/tex] we can use the formula [tex]m = \frac{dy}{dx}[/tex] where [tex]dy[/tex] is the difference in [tex]y[/tex] between two points and [tex]dx[/tex] is the difference between [tex]x[/tex].
Information we can get from the graph given: [tex]c=-6[/tex]. Since [tex]c[/tex] is the point at which the line crosses the [tex]y[/tex]-axis.
To find [tex]m[/tex] let's get two points from the graph.
Point 1: [tex](4,-7)[/tex]
Point 2: [tex](8,-8)[/tex]
Now use the equation [tex]m = \frac{dy}{dx}[/tex].
[tex]m = \frac{-7 - (-8)}{4-8} = -\frac{1}{4}[/tex].
Now we have [tex]m[/tex] and [tex]c[/tex], let's put them back into the general equation.
[tex]y=-\frac{1}{4} x-6[/tex]
