In the xy-plane, the point `(4,7)` lies on the line t, which is perpendicular to the line `y =-4/3x+6.` What is the equation of line t ?

Options

A. `y =3/4x +4`
B. `y = -4/3x +4`
C. `y =3/4x +7`
D. `y =-3/4 x +4`

Answer

A

Explanation

The first useful pices of information is that the slope of the line perpendicular to line t is `-4/3.` Perpendicular lines have negative reciprocal slopes, so the slope of line t is `3/4.` Eliminate (B) and (D) because they have the incorrect slopes.
Plug the values for the slope and the coordinate point `(4,7)` into the slope-intercept equation to solve for b:
`7= 3/4(4) +b`
`7=3+b`
`7-3=b`
`b=4`
Eliminate (C ) because it does not have the correct y-intercept. Choice (A) is correct.