Line f in th exy-plane passes through the origin and has a slope of `-2/5.` Line z is perpendicular to line f and passes through the point `(6,2).` Which of the following is the equation of line z ?

Options

A. `y =-1/5x`
B. `y =-2/5x -13`
C. `y =5/2x`
D. `y =5/2x-13`

Answer

D

Explanation

This question provides an equation for a line perpendicular to line z and a coordinate point for line `z, (6,2).` The opposite sign reciprocal of the slope of the perpendicular line, `5/4,` is the slope of line z. Eliminate (A) and (B) because they have the incorrect slope.
Plug the values for the slope and the coordinate point `(6,2)` into the slope-intercept equation to solve for b:
`2=5/2(6) +b`
`2=15+b`
`2-15 =b`
`b =-13`
Plug the values for the slope and the y-intercept into the slope-intercept equation to get `y =5/2x-13.` (D) is correct.
You can save a little time if you eliminate (C ) as soon as you see that `b ne 0,` which you should be able to tell as soon as youi see that `2 =15+b.`