39. Write the equation of a line that is perpendicular to the given line and that passes through the given point.

y + 2 = 1/3(x – 5); (–4, 3)

A.)y = –3x + 15
B.)y = –3x – 9
C.)y = –4x + 3
D.)y = –1/3x – 11

I don't know how to do this.

sure you do. The given line has slope 1/3 and passes through (5,-2).

You want a line with slope -3 that passes through (-4,3).

y-3 = -3(x+4)
y = -3x -9

(B)

To find the equation of a line that is perpendicular to the given line and passes through the given point, we can follow these steps:

1. Determine the slope of the given line by putting the equation in slope-intercept form, y = mx + b. The coefficient of x will be the slope of the line.

Given line: y + 2 = 1/3(x - 5)

Rewriting it in slope-intercept form: y = (1/3)x - 5/3

The slope of the given line is 1/3.

2. Since a line perpendicular to another line has a negative reciprocal slope, we need to find the negative reciprocal of 1/3.

Negative reciprocal of 1/3 is -3.

3. Use the point-slope form of a line to find the equation of the perpendicular line.

Point-Slope Form: y - y1 = m(x - x1)

Given point: (-4, 3) (x1, y1)

Using the negative reciprocal slope, m = -3, and the given point (-4, 3), the equation becomes:

y - 3 = -3(x - (-4))

Simplifying:

y - 3 = -3(x + 4)

y - 3 = -3x - 12

Adding 3 to both sides:

y = -3x - 12 + 3

Simplifying again:

y = -3x - 9

So, the equation of the line that is perpendicular to the given line and passes through the point (-4, 3) is y = -3x - 9.

Comparing the equation with the given options, the correct answer is B.) y = -3x - 9.