For question 23 i struggle with understanding why the equation is y= -1/2x + c
A = (-2, 0) B = (0,4) the slope of this line is 2
So....a perpendicular line to this will have the slope = -1/2
And since this line passes through (5, -1) we have that
y = (-1/2)(x - 5) - 1
y = (-1/2)x + 5/2 - 1
y = (-1/2)x + 3/2
The "c" comes from the standard form of a line.....
Ax + By = C
Subtract Ax from both sides
By = -Ax + C divide both sides by B
y = (-A/B) x + C/B
Using what we know -A/B = the slope = -1/2 y = -1 and x = 5
-1 = (-1/2) (5) + C/B
3/2 = C/B where C/B = "c"