Answer:
[tex]\displaystyle \frac{7}{8}[/tex]
Step-by-step explanation:
Hi there!
First, find the slope of Line p:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (5,−3) and (−2, 5):
[tex]\displaystyle m=\frac{-3-5}{5-(-2)}\\\\\displaystyle m=\frac{-3-5}{5+2}\\\\\displaystyle m=\frac{-8}{7}[/tex]
Therefore, the slope of Line p is [tex]\displaystyle- \frac{8}{7}[/tex].
Perpendicular lines always have slopes that are negative reciprocals, such as 1/2 and -1/2, and 3/4 and -4/3.
Knowing this, the slope of a line perpendicular to Line p would be the negative reciprocal of [tex]\displaystyle- \frac{8}{7}[/tex], which is [tex]\displaystyle \frac{7}{8}[/tex].
I hope this helps!
