Question

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

A/ y=-4/3x+12
b/ Y=4/3+12
C/ y=-3/4x+12
d/ y=3/4x+12

Answer 1

Option A

The line
`y = (-4)/(3)x + 12` is perpendicular to
`y = (3)/(4)x - 3`

Solution:

Given that line is
`y = (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 = (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,

`(3)/(4) * a = -1`

`a = (-4)/(3)`

Now look at the options and compare with slope intercept form and find out which option has the slope "m" =
`(-4)/(3)`

Option A
`y = (-4)/(3)x + 12` has the slope
`(-4)/(3)`

Thus option A is correct