Question

The line segment ( A B ) has endpoints of A(-4,3) and B(2,7) . Determine the equation of a line parallel to ( A B ) and passing through the point (4,-2) .

Answer 1

To find the equation of a line parallel to (AB) and passing through the point (4,-2), calculate the slope of (AB) and then use the point-slope formula with the given point.

Step-by-step explanation:

To determine the equation of a line parallel to (AB) and passing through the point (4,-2), we need to find the slope of the line (AB) first. The slope can be calculated using the formula:

Slope = (change in y-coordinates) / (change in x-coordinates).

In this case, the coordinates of A are (-4,3) and the coordinates of B are (2,7). Thus, the slope of (AB) is (7-3) / (2 - (-4)) = 0.67.

Since the parallel line will have the same slope, we can use the point-slope formula to find its equation. The formula is:

y - y1 = slope * (x - x1), where (x1, y1) is the given point.

With the point (4,-2) and the slope 0.67, the equation of the line parallel to (AB) would be y - (-2) = 0.67 * (x - 4).