Original Slope: -3/4
Perpendicular Slope: 4/3
Step-by-step explanation:
Hey there! In order to find slope we must find the change in y and divide it by the change in x(use formula below). Perpendicular slope is the negative reciprocal of the original slope(flip the fraction and multiply by -1).
Slope formula : [tex]\boxed{m = \frac{{y_2 - y_1}}{{x_2 - x_1}}}[/tex]
Where:
- [tex]\text{m represents the slope }[/tex]
- [tex]x_1 \text{ represents the x-value of the first coordinate you selected}[/tex]
- [tex]y_1 \text{ represents the y-value of the first coordinate you selected}[/tex]
- [tex]x_2 \text{ represents the x-value of the second coordinate you selected}[/tex]
- [tex]y_2 \text{ represents the y-value of the second coordinate you selected}[/tex]
Solving:
Pick two coordinate points and plug it into the formula I chose (0,1) and (4,-2):
[tex]{m = \frac{{y_2 - y_1}}{{x_2 - x_1}}}[/tex]
[tex]{m = \frac{{-2 - 1}}{{0 - 4}}}[/tex]
[tex]\boxed{m = -\frac{{3}}{{4}}}[/tex]
Which gives us our answer to the Original Slope.
Now for perpendicular slope(negative reciprocal):
[tex]-1(\frac{1}{(-3/4)}) = \boxed{4/3}[/tex]
That's it!
