Question

A linear function intersects the x-axis at - 5 and the y - axis at - 3 . What is the equation of the function ?

Answer 1

If the function intersects the x-axis at -5, we have the point (-5, 0).

If the function intersects the y-axis at -3, we have the point (0, -3).

Then, we can use these points in the slope-intercept form of the linear equation:

`y=mx+b`

Using the points, we have:

`\begin{gathered} (0,-3)\colon \\ -3=0m+b \\ b=-3 \\ \\ (-5,0)\colon \\ 0=-5m-3 \\ 5m=-3 \\ m=-(3)/(5) \end{gathered}`

So the equation of the function is:

`y=-(3)/(5)m-3`