Question

What line is perpendicular to y=3/4x-3

Answer 1

Option A

The line $y = \frac{-4}{3}x + 12$ is perpendicular to $y = \frac{3}{4}x - 3$

Solution:

Given that line is $y = \frac{3}{4}x - 3$

We have to find the line perpendicular to this line.

The given line equation is in form of slope-intercept form

The slope-intercept form is given as:

y = mx + c

Where "m" is the slope of the line and "c" is the y-intercept

On comparing the given equation with slope-intercept form, we get

$m = \frac{3}{4}$

If a line is perpendicular to another line, then the product of their slopes will always be -1

Let the slope of line which is perpendicular to given line be "a"

Then we get,

$\frac{3}{4} \times a = -1$

$a = \frac{-4}{3}$

Now look at the options and compare with slope intercept form and find out which option has the slope "m" = $\frac{-4}{3}$

Option A $y = \frac{-4}{3}x + 12$ has the slope $\frac{-4}{3}$

Thus option A is correct