Answer:
y = 1/5x -11
Step-by-step explanation:
You want the slope-intercept equation of the line perpendicular to y=-5x+9 that goes through the point (20, -7).
Slope-intercept form
The slope-intercept form of the equation for a line is ...
y = mx +b . . . . . . . . where m is the slope and b is the y-intercept
This can be solved to find the y-intercept from a point on the line:
b = y -mx
Comparing this form to the given equation, you see the given line has a slope of m = -5.
Perpendicular line
The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line:
slope = -1/(-5) = 1/5
Y-intercept
The y-intercept of the desired line can be found using the equation for b above. The y-intercept of the line with slope 1/5 through point (x, y) = (20, -7) is ...
b = y -mx = (-7) -1/5(20) = -7 -4
b = -11
Now, we have the slope and intercept of the desired line, so we can write its equation:
y = 1/5x -11
