To find the equation for the line in slope-intercept form y= mx + b, perpendicular to the line shown and passing through (6, -6):
The slope of the blue line is the rise (change in y) divided by run (change in x)
Choosing two points on the line (0, -6) and (2,0)
Slope = (0 - (-6)) / (2 - 0) = 6 / 2 = 3
The slope of our perpendicular line will be the opposite inverse, so:
m = -1/3
We have the point (6, -6) so we can solve for b
y = mx + b
-6 = (-1/3)*6 + b
-6 = -2 + b
b = -4
We know that m= (-1/3) and b= -4, so:
y = (-1/3)x - 4
This is definitely the correct answer. None of the above answers describe the line that is perpendicular to the blue line and passes through (6, -6). Make sure you wrote the options down correctly.