To find 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. The negative reciprocal of 8/3 is -3/8.
Using the point-slope form of a line, we can write the equation of the line that is perpendicular to the given line and passes through the given point (-2, 3):
y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope
Substituting the values into the equation, we have:
y - 3 = -3/8 (x - (-2))
y - 3 = -3/8 (x + 2)
y - 3 = -3/8x - 3/4
y = -3/8x - 3/4 + 3
y = -3/8x - 3/4 + 12/4
y = -3/8x + 9/4
Therefore, the equation of the line that is perpendicular to the given line and passes through the given point is y = -3/8x + 9/4.
The correct answer is D. y + 3 = 3/8 (x - 2).
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