Question

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

A) y = 3x - 10
B) y = -1/3x + 2
C) y = -3x - 10
D) y = 1/3x - 2

Answer 1

The correct equation of a line that is perpendicular to y = -3x + 2 and passes through the point (3, -1) is y = ⅓x - 2.

Step-by-step explanation:

The question involves finding the equation of a line that is perpendicular to a given line and passes through a specific point. The given equation of the line is y = -3x + 2. To be perpendicular, the new line must have a slope that is the negative reciprocal of the original slope of -3, which is ⅓. Hence, the slope of the line we are looking for is ⅓. Now, using the point (3, -1) that the new line passes through, we can use the point-slope form to find the equation:

y - y1 = m(x - x1) where (x1, y1) is the point (3, -1) and m is the slope ⅓.

Substituting these values, we get:

y + 1 = ⅓(x - 3)

Now, we distribute the slope on the right side:

y + 1 = ⅓x - 1

Subtracting 1 from both sides to solve for y:

y = ⅓x - 2

So, the correct equation of the line is y = ⅓x - 2, which corresponds to option D.