wright the equation of a line that is perpendicular to the given line and that passes through the given point

Question

y-4=5/2 (x+3);(-7,8)

y-8=-2/5 (x-7)
y-8=2/5(x-7)*
y-8=-2/5(x+7)
y-8=2/5(x+7)

i’m not sure please help thank you:-)

Answer 1

Perpendicular lines have slopes that are opposite reciprocals of each other
So if your given line has slope 5/2 as shown, then the slope of the perpendicular must be -2/5
This immediately rules out b) and d)
leaving a) and c) , [your choice was b)]
sub in the given point, and see in which equation it satisfies.