Simon wanted to find the equation of a line that passes through (–6, 5) and is perpendicular to the graph of 3x + 2y = –11. His work is shown below.
1. 3x + 2y = –11 written in slope-intercept form is y = -3/2x - 11/2 , so the slope is -3/2.
2. The slope of the perpendicular line is -2/3.
3. Substitute the point and the new slope into point-slope form to get y – 5 = -2/3(x – (–6)).
4. Simplifying, the line is y – 5 = -2/3(x + 6).
Is Simon’s work correct?

A. No, the slope of the line 3x + 2y = –11 is not .
B. No, the slope of the line perpendicular to the line 3x + 2y = –11 should be .
C. No, he did not substitute the point and the slope into point-slope form correctly.
D. Yes, the work is correct.

The slope of a perpendicular line is the opposite of the reciprocal of the slope of the original. Simon correctly computed the original line's slope to be -3/2. He correctly computed the reciprocal of that to be -2/3, but failed to recognize that the slope of the perpendicular line is the opposite of this, 2/3.

Simon's work is correct otherwise.

Answer Link