Question

A linear function goes through the points (4, 2) and (4, 4). A second linear function has not been found. Where is it? Which is the larger of the two slopes?

A) The second linear function is at (4, 3) with a slope of -2/5.
B) The second linear function is at (4, 2) with a slope of -3/4.
C) The second linear function is at (4, 4) with a slope of -4/3.
D) The second linear function is at (4, 5) with a slope of -5/2.

Answer 1

A linear function goes through two points with the same x-coordinate, creating a vertical line. The second linear function can be found anywhere on the same vertical line. The first linear function has a larger slope.

Step-by-step explanation:

In this scenario, we are given that a linear function goes through the points (4, 2) and (4, 4). Since both points have the same x-coordinate, the function is a vertical line passing through the x = 4 axis. The second linear function can be found by choosing any other point on the same vertical line, as long as it has a different y-coordinate. In this case, the second linear function is at (4, 3) with a slope of -2/5.

The slope of a linear function represents the rate of change between two points on the line. In this case, the first linear function has a slope of 0, since it is a vertical line. The second linear function has a slope of -2/5, which is smaller than 0. Therefore, the first linear function has a larger slope.