Question

Write an equation for a line perpendicular to y=-5x-3 and passing through the point (15,4)

Answer 1

`y=(1)/(5)x+1`

1) We need to consider the fact that perpendicular lines described by linear functions have opposite and reciprocal slopes when compared to the original linear function.

2) So we can state that the perpendicular line to y=-5x-3 has a slope of :

`m=(1)/(5)`

3) Now, the next step is to plug into the Slope-intercept form the following point (15,4) and then find the y-intercept:

`\begin{gathered} y=mx+b \\ 4=(1)/(5)(15)+b \\ 4=3+b \\ 4-3=b \\ b=1 \end{gathered}`

4) Thus, the equation of a perpendicular line to the line described by the linear function y=-5x-3 is:

`y=(1)/(5)x+1`