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Question

A coordinate plane shows two intersecting lines. The solid line slopes upward from left to right. The dotted line slopes downward from left to right. The lines intersect at approximate coordinates left parenthesis 0.8 comma negative 1.3 right parenthesis. The solid line has a y-intercept at left parenthesis 0 comma negative 3 right parenthesis, and passes through unlabeled points at left parenthesis 1 comma negative 1 right parenthesis, an x-intercept at left parenthesis 1.5 comma 0 right parenthesis, left parenthesis 2 comma 1 right parenthesis, and left parenthesis 3 comma 3 right parenthesis. The dotted line passes through unlabeled points at left parenthesis negative 4 comma 1 right parenthesis, an x-intercept at left parenthesis negative 2 comma 0 right parenthesis, a y-intercept at left parenthesis 0 comma negative 1 right parenthesis, left parenthesis 2 comma negative 2 right parenthesis, and left parenthesis 4 comma negative 3 right parenthesis. On the coordinate plane, both axes range from negative 4 to 4.

Compare the linear additive relationship shown. Choose the statement that best describes the graphs. Enter the number of the correct response.

1) The graphs intersect at the x
-intercepts.

2) The graphs have slopes that are negative reciprocals, so the lines are perpendicular.

3) The graphs both have positive slopes but different y
-intercepts.

4) The graphs both have negative y
-intercepts, so the lines are perpendicular.

(1 point)

Answer 1

The correct response is:

2. The graphs have slopes that are negative reciprocals, so the lines are perpendicular.

This statement best describes the relationship between the two lines based on the information provided. The solid line slopes upward while the dotted line slopes downward, indicating that they are likely to be perpendicular to each other.