An equation in the slope-intercept form is f(x) = mx + b, where m is the slope and b is the y-intercept.
Given:
slope = m = 5
The equation is f(x) = 5x + b
To find b, let's use the point (-2, -8), substituting x by -2 and f(x) by -8.
[tex]\begin{gathered} f(x)=5x+b \\ f(-2)=-8 \\ -8=5*(-2)+b \\ -8=-10+b \\ \text{ Adding 10 to both sides:} \\ -8+10=-10+b+10 \\ 2=b \end{gathered}[/tex]Answer:
The equation of the line is f(x) = 5x - 2.
