Question

What is the equation of the line that is perpendicular to the line y = -1/2x + 1 and goes through the point (3, 2)?

A) y = 2x + 1
B) y = x/2 - 4
C) y = -x + 1
D) y = -2x - 7

Answer 1

The equation of the line perpendicular to y = -1/2x + 1 that passes through (3, 2) is y = 2x - 4. This is found by using the negative reciprocal of the original line's slope and applying the point-slope formula.

Step-by-step explanation:

The question asks to find the equation of a line that is perpendicular to the line y = -1/2x + 1 and passes through the point (3, 2). To find a line perpendicular to a given line, we must use a slope that is the negative reciprocal of the original line's slope. The slope of the given line is -1/2, so the slope of the perpendicular line must be 2 (the negative reciprocal of -1/2).

With a slope of 2 and passing through the point (3, 2), the equation can be found using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Plugging in the values, we get:

y - 2 = 2(x - 3)

Simplify this to get the equation in slope-intercept form:

y = 2x - 6 + 2

y = 2x - 4

Therefore, the correct equation is y = 2x - 4, which corresponds to option B.