The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m reresents slope
c represents y intercept
The equation of the given line is
y = x/3 + 3
By comparing both equations,
m = 1/3
recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Recall, the negative reciprocal of 1/3 = - 3/1 = - 3 This means that the slope of the perpendicular line passing through the point (- 1, - 2) is
m = - 3
We would find the y intercept, c by substituting m = - 3, x = - 1 and y = - 2 into the slope intercept equation. We have
- 2 = - 3 * - 1 + c
- 2 = 3 + c
Subtracting 3 from both sides,
- 2 - 3 = 3 - 3 + c
c = - 5
By substituting m = - 3 and c = - 5 into the slope intercept equation, the equation of the perpendicular line is
y = - 3x - 5