Question

PLEASE HELP ME SOLVE

Write an equation of the line passing through point p(-1,3) that is perpendicular to y=4x-7

Answer 1

Two lines are perpendicular if their slope m and m' satisfy the equation

`mm'=-1`

The slope of the given line is 4, because the line is written in the slope-intercept y=mx+q, where m is the slope.

So, the perpendicular slope is

`4m'=-1 \iff m'=-(1)/(4)`

So, we want a line with slope -1/4 and passing through (-1,3). We can use the formula

`y-b=m(x-a)`

for the line passing trough (a,b) with slope m:

`y-3=-(1)/(4)(x+1) \iff y=-(1)/(4)x-(1)/(4)+3\iff y=-(1)/(4)x+(11)/(4)`