Question

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−23x+5 ?

Answer 1

Answer:

$y-1=\frac{1}{23} (x-8)$

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point (8,1) and a slope from the equation y=-23x+5. We will chose point-slope since we have a point and slope.

Point slope:$y-y_1=m(x-x_1)$

$m\neq -23$ in our new equation because it us perpendicular to it. This means we will need to change it into its negative reciprocal which is $m=\frac{1}{23}$.

We will substitute $m=\frac{1}{23}$ and $x_1=8\\y_1=1$.

$y-1=\frac{1}{23} (x-8)$.

This is the equation of the line perpendicular to y=-23x+5 that crosses through (8,1).