Write the equation of a line that is perpendicular to y=2/7x +9 and that passes through the point (4,-6).

Question

asked Oct 8, 2021 225k views

1 Answer

Leonardo Delfino · Answer 1 · 2021-10-14T16:09:09+0000

Answer:

y=-(7)/(2)x+8

Explanation:

Given the equation

$y\:=\:(2)/(7)x+9$

comparing the equation with the slope-intercept form

y =mx+b

Here,

so the slope of the line is 2/7

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

the slope of the perpendicular line will be: -7/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (4,-6) is:

$y-y_1=m\left(x-x_1\right)$

$y-\left(-6\right)=(-7)/(2)\left(x-4\right)$

$y+6=(-7)/(2)\left(x-4\right)$

$y+6-6=(-7)/(2)\left(x-4\right)-6$

y=-(7)/(2)x+8