Question

Write an equation of the line containing the given point and perpendicular to the given line.
(8,-3); 8x + 5y=4
The equation of the line is y = ?

Answer 1

So the original equation in y=mx+b form is:
\[y=(-8/5)x + 4\]
The slope of the perpendicular line will be the inverse of the negative of this slope. So we can substitute the given point into the following equation:
\[y=(5/8)x+b\]
Giving us:
\[-3=(5/8)8+b\]
\[-3=5+b\]
b=-8
With a final answer of:
\[y=(5/8)x-8\]

Answer 2

Thank you!