Question

he function f(x) is graphed below.

mc013-1.jpg

What is the equation of the line that is perpendicular to f(x) and passes through the point (4, –6)?
4x + 3y = –2
3x + 4y = –12
4x – 3y = 34
3x – 4y = 36

Answer 1

All four given lines pass through (4, −6), so we must match slopes. Put each in slope-intercept form:
- A: 4x + 3y = −2 → y = (−4/3)x − 2/3 (slope −4/3)
- B: 3x + 4y = −12 → y = (−3/4)x − 3 (slope −3/4)
- C: 4x − 3y = 34 → y = (4/3)x − 34/3 (slope 4/3)
- D: 3x − 4y = 36 → y = (3/4)x − 9 (slope 3/4)

If f(x) has slope 3/4, a perpendicular line has slope −4/3, so the correct equation is 4x + 3y = −2.