Answer:
y = [tex]-\frac{1}{3} x[/tex] + 2
Step-by-step explanation:
The slope of the line that has an x intercept of (2,0) and y-intercept of (0,-6) is:
Slope(s) = Change in y ÷ change in x
s = [tex]\frac{0 - -6}{2 - 0}[/tex] = 3
The slope of the perpendicular line to this line with slope of 3 has to have a slope of -1 ÷ 3 = [tex]-\frac{1}{3}[/tex]
Reason: The product of slopes of lines perpendicular to each other have to be -1
So the slope of the perpendicular line that passes through (-6,4) is [tex]-\frac{1}{3}[/tex]
As mentioned earlier, we derive a slope of a line by dividing the change in y by the change in x
Taking another point (x,y) on the line,
[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x - -6}[/tex]
[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x + 6}[/tex]
y - 4 = [tex]-\frac{1}{3}[/tex]x - 2
y = [tex]-\frac{1}{3}[/tex]x + 2
