Option A
The line [tex]y = \frac{-4}{3}x + 12[/tex] is perpendicular to [tex]y = \frac{3}{4}x - 3[/tex]
Solution:
Given that line is [tex]y = \frac{3}{4}x - 3[/tex]
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
[tex]m = \frac{3}{4}[/tex]
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,
[tex]\frac{3}{4} \times a = -1[/tex]
[tex]a = \frac{-4}{3}[/tex]
Now look at the options and compare with slope intercept form and find out which option has the slope "m" = [tex]\frac{-4}{3}[/tex]
Option A [tex]y = \frac{-4}{3}x + 12[/tex] has the slope [tex]\frac{-4}{3}[/tex]
Thus option A is correct
