Question

Line p has an equation of y = 2x – 2. Line q includes the point (6, 1) and is perpendicular to line p. What is the equation of line q?

A) y = -2x + 13
B) y = -2x + 14
C) y = -2x + 15
D) y = -2x + 16

Answer 1

The equation of line q, which is perpendicular to line p with an equation y = 2x – 2 and passes through point (6, 1), is y = -2x + 13, corresponding to option A.

Step-by-step explanation:

The student's question relates to finding the equation of line q, which is perpendicular to line p with the equation y = 2x – 2 and passes through the point (6, 1). Since line q is perpendicular to line p, the slope of line q will be the negative reciprocal of the slope of line p. Given the slope of line p is 2, the slope of line q will be –2.

To find the equation of line q, we use the point-slope form y – y1 = m(x – x1), where (x1, y1) is the point through which line q passes and m is the slope of line q. Substituting the given point (6, 1) and the slope –2 into the equation:

y – 1 = –2(x – 6)

Expanding and simplifying:

y = –2x + 12 + 1

y = –2x + 13

Therefore, the equation of line q is y = –2x + 13, which matches option A.