Question

Which statement is true about a line that runs parallel to the x-axis and passes through the point (-4,13)?

(1) It has a slope of zero and an equation of x=-4.
(2) It has an undefined slope and an equation of x=-4.
(3) It has a slope of zero and an equation of y=13.
(4) It has an undefined slope and an equation of y=13.

Answer 1

The line that runs parallel to the x-axis and passes through the point (-4,13) has an undefined slope and an equation of y=13.

Step-by-step explanation:

The correct statement is option (4): It has an undefined slope and an equation of y=13.

A line that runs parallel to the x-axis is horizontal. A horizontal line has an undefined slope because the slope is the change in y divided by the change in x, but since the line does not change in the y-direction, the change in y is zero. Therefore, any division by zero results in an undefined slope.

Since the line passes through the point (-4,13), the equation of the line is y=13, where the y-coordinate remains constant.

Answer 2

#3

Step-by-step explanation:

If it is parallel to the x axis it has 0 slope, and that means its y=y value. The y value here is 13 so,

It has a slope of zero and an equation of y=13