Question

A line passes through (4, 0) and is perpendicular to the line that goes through (1, 2) and (3, 10).

a. y = -2x + 10
b. y = 2x - 6
c. y = 1/2x - 1
d. y = -1/2x + 2

Answer 1

To find the equation of the line perpendicular to the given line passing through (1, 2) and (3, 10), we need to find the negative reciprocal of the slope of the given line. The slope of the given line is 4, so the slope of the perpendicular line is -1/4. Using the point (4, 0), we can write the equation of the perpendicular line as y = -1/4x + 1.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The slope of the given line is found by using the formula: m = (y2 - y1) / (x2 - x1). So the slope of the given line passing through (1, 2) and (3, 10) is m = (10 - 2) / (3 - 1) = 8 / 2 = 4.

Since the line we are looking for is perpendicular to the given line, its slope will be the negative reciprocal of 4, which is -1/4.

Using the point (4, 0) on the line, we can write the equation of the line in point-slope form as y - y1 = m(x - x1) where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get y - 0 = -1/4(x - 4) which simplifies to y = -1/4x + 1. So the correct answer is d. y = -1/4x + 1.