Question

what is the equation of the line that passes through (5, -2) and (-3, 4)

Answer 1

Find the rate of change (slope).
\[\frac{ 4-(-2) }{ -3-5 }=\frac{ 6 }{ -8} or \frac{ 3 }{ -4 }\]
I am assuming you're using slope intercept form here.
y=mx+b
m=3/-4
Substitute a coordinate for x and y to solve for b.
-2=3/-4(5)+b
-2=15/-4+b
Add 15/4 to both sides to solve for b.
15/4-2=b
Find an LCD and simplify
15/4-8/4=b
b=7/4
Your equation is y=3/-4x+7/4