Question

Given slope=5, passing through (-2,-8) What is the point slope form of the equation? What is the slope intercept form of the equation written in function notation?

Answer 1

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.

`\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}`

Answer:

The equation of the line is f(x) = 5x - 2.