Question

What is the equation in slope-intercept form for a line that is perpendicular to y = -2x + 6 and passes through the point (3, 2)?

A) y = 2x + 6
B) y = -1/2x + 4
C) y = -2x - 4
D) y = 1/2x - 4

Answer 1

The equation in slope-intercept form for a line perpendicular to y = -2x + 6 and passing through the point (3, 2) is y = 1/2x - 4.

Step-by-step explanation:

The equation of a line that is perpendicular to y = -2x + 6 must have a slope that is the negative reciprocal of -2. The negative reciprocal of -2 is positive 1/2. The line must also pass through the point (3, 2). Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through, we plug in our values: y - 2 = 1/2(x - 3). Simplifying this equation gets us y = 1/2x - 1/2(3) + 2, which further simplifies to y = 1/2x - 4.