Answer:
[tex]y-1=\frac{1}{23} (x-8)[/tex]
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:[tex]y-y_1=m(x-x_1)[/tex]
[tex]m\neq -23[/tex] in our new equation because it us perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=\frac{1}{23}[/tex].
We will substitute [tex]m=\frac{1}{23}[/tex] and [tex]x_1=8\\y_1=1[/tex].
[tex]y-1=\frac{1}{23} (x-8)[/tex].
This is the equation of the line perpendicular to y=-23x+5 that crosses through (8,1).
