Answer:
f(x) = -(1/2)x + 4
Explanation:
Let's look for an equation for a straight line of the form y=mx+b, where m is the slope and b is the y-intercept.
We are told this line is perpendicular to a line that has two points identified: (4,0) and (0,-8).
To start, we need to determine the slope of the second line, Slope is the Rise/Run of a line. We can calculate both from the two points given:
(0,-8) to (4,0)
Rise (change in y) = (0-(-8)) = 8
Run = change in x = (4 - 0) = 4
Slope = Rise/Run = (8/4) or 2
The reference line has a slope of 2. Any line that is perpendicular to this line will have a slope that is the negative inverse of the reference line:
negative inverse of slope 2 is slope -(1/2)
The new line has a slope of -(1/2).
We can write y = -(1/2)x + b
Any value of b will still produce a perpendicular line to the reference line. But we are told the new line goes through point (-8,8). To find a value of b that moves the line to go though (-8,8), just enter these coordinates into the equation above and solve for b:
y = -(1/2)x + b
8 = -(1/2)(-8) + b for (-8,8)
8 = -(1/2)(-8) + b
8 = 4 + b
b = 4
The equation becomes y = -(1/2)x + 4
For illustration purposes, lets add the line with slope of 2 that goes through points (4,0) and (0,-8): y = 2x -8
See the attached graph.