Question

What is the equation of a line perpendicular to y=-2/5X-1 that passes through (2,-8)

Answer 1

Answer:

$y=\frac{5}{2}x-13$

Step-by-step explanation:

Given the equation

$y=-\frac{2}{5}x-1$

comparing the equation with the slope-intercept form$y=mx+b$

Here,

• m is the slope

• b is the intercept

so the slope of the line is m = -2/5

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: 5/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (2,-8) is:

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

$y-\left(-8\right)=\frac{5}{2}\left(x-2\right)$

$y+8=\frac{5}{2}\left(x-2\right)$

subtract 8 from both sides

$y+8-8=\frac{5}{2}\left(x-2\right)-8$

$y=\frac{5}{2}x-13$