Question

Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A line with slope 3 can be parallel to a line with slope – 3. Choose the correct answer below.

A. The statement is false. A line with slope 3 can be perpendicular to a line with slope - 3.
B. A line with slope 3 can be parallel to a line with slope 1/3
C. A line with slope 3 can only be parallel to a line with slope

Answer 1

The statement is false because a line with the slope of 3 can only be parallel to another line with the same slope, and it can be perpendicular to a line with a slope of -3.

Step-by-step explanation:

The statement "A line with slope 3 can be parallel to a line with slope – 3" is false. Two lines can only be parallel if they have the exact same slope. Therefore, a line with a slope of 3 can only be parallel to another line that also has a slope of 3.

The correct answer is:

A. The statement is false. A line with slope 3 can be perpendicular to a line with slope -3.

This is because perpendicular lines have slopes that are negative reciprocals of each other. Since 3 and -3 are opposite numbers and also reciprocals of each other when considering 3 as 3/1 and -3 as -1/3, the slopes indicate that the lines would be perpendicular, not parallel.