Question

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

Answer 1

Answer:

$y=-\frac{7}{2}x+8$

Step-by-step explanation:

Given the equation

$y\:=\:\frac{2}{7}x+9$

comparing the equation with the slope-intercept form

$y =mx+b$            

Here,

• m is the slope

• y is the intercept

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:

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

$y-\left(-6\right)=\frac{-7}{2}\left(x-4\right)$

$y+6=\frac{-7}{2}\left(x-4\right)$

$y+6-6=\frac{-7}{2}\left(x-4\right)-6$

$y=-\frac{7}{2}x+8$