Question

Given a point P = (5, 4) and perpendicular to y = (3/8)x - 5, find the equation.

A. y = (-8/3)x + (64/3)
B. y = (8/3)x - (64/3)
C. y = (-3/8)x + (19/8)
D. y = (3/8)x - (19/8)

Answer 1

The correct equation of the line perpendicular to y = (3/8)x - 5 and through point P = (5, 4) is y = (-8/3)x + (64/3), which is answer option A.

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and that passes through a specific point, you need to take the following steps:

1. Identify the slope of the original line. The slope of the line y = (3/8)x - 5 is 3/8.
2. Determine the slope of the perpendicular line. The slope of the perpendicular line will be the negative reciprocal of the original slope, so the new slope will be -8/3.
3. Use the point-slope form of the equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the point P. Plugging in the point P = (5, 4) and the slope -8/3, we get:
4. y - 4 = (-8/3)(x - 5)
5. Multiply both sides by 3 to clear the fraction: 3y - 12 = -8x + 40
6. Add 12 to both sides and add 8x to both sides to get the equation in slope-intercept form:
7. y = (-8/3)x + (64/3)

Therefore, the correct answer is A. y = (-8/3)x + (64/3).