Question

For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the x-axis? Circle your answer(s). Without plotting them, explain how you know.

a. (1.4, 2.2) and (4.1, 2.4)
b. (3, 9) and (8, 9)
c. (1 1/4, 2) and (1 1/4, 8)

Answer 1

The correct answer is (b).

Explanation:

A line is parallel to the
`x` axis if it has a slope equal zero. Then if we compute the slope of the line that joins the points
`(3,9), (8,9)` then

`m=(y_(2)-y_(1))/(x_(2)-x_(1))=(9-9)/(3-8)=(0)/(-5)=0`

This implies that the line which that joins this points is parallel to the x-axis.

Observe that the slopes of the lines corresponding to the other items are nonzero.