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 that is perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of 8/3, so the negative reciprocal is -3/8.

Using the point-slope form of a linear equation, we can write the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the negative reciprocal of the slope.

Plugging in the values, we have:

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

Rearranging the equation, we get:

y - 3 = -3/8x - 3/4

Adding 3 to both sides:

y = -3/8x - 3/4 + 3

Finding a common denominator:

y = -3/8x - 3/4 + 12/4

Combining the fractions:

y = -3/8x + 9/4

Therefore, the equation of the line that is perpendicular to the given line and passes through the point (-2, 3) is:

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