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.
Accepted Solution
A:
Answer:B. No, the slope of the line perpendicular to the line 3x + 2y = –11 should be 2/3.Step-by-step explanation: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.