Question

Choose the point-slope form of the equation below that represents the line that passes through the points (−6, 4) and (2, 0).

a. y − 4 = − 1/2 (x + 6)
b. y − 4 = 2(x + 6)
c. y + 6 = − 1/2 (x − 4)
d. y + 6 = 2(x − 4)

Answer 1

To find the equation of a line passing through two points in point-slope form, we calculate the slope and use the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of a point on the line. The equation representing the line passing through the points (-6, 4) and (2, 0) is y - 4 = -1/2 (x + 6).

Step-by-step explanation:

To find the equation of a line in point-slope form, we use the formula: y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of a point on the line. Given the points (−6, 4) and (2, 0), we can calculate the slope as follows:

1. Slope = (y2 - y1) / (x2 - x1)
2. Slope = (0 - 4) / (2 - (-6))
3. Slope = -4 / 8
4. Slope = -1/2

The point-slope form equation representing the line passing through these points is y - 4 = -1/2 (x + 6). Therefore, the correct answer is a. y - 4 = -1/2 (x + 6).