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

y - 3 = 8/3 (x + 2); (-2, 3)

A. y + 3 = -3/8 (x - 2)
B. y - 3 = -3/8 (x + 2)
C. y - 2 = -3/8 (x + 3)
D. y + 3 = 3/8 (x - 2)

1 answer

To find the equation of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.

The given line has the slope 8/3.

The negative reciprocal of 8/3 is -3/8. So, the slope of the perpendicular line is -3/8.

Now, let's plug in the values into the point-slope form of a line to find the equation of the perpendicular line:

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

Using the point (-2, 3) and slope -3/8, the equation becomes:

y - 3 = -3/8 (x - (-2))

Simplifying further:

y - 3 = -3/8 (x + 2)

Therefore, the correct equation is:

D. y + 3 = 3/8 (x - 2)