Question

Given the point (3, -4) on the graph below, which of the statements below is true?

A) The line y = -4 is perpendicular to the y-axis and has an undefined slope.
B) The line y = -4 is parallel to the y-axis and has a slope of zero.
C) The line x = 3 is perpendicular with the x-axis and has an undefined slope.
D) The line x = 3 is perpendicular to the y-axis and has a slope of zero.

Answer 1

The correct answer is B) The line y = -4 is parallel to the x-axis and has a slope of zero, as horizontal lines have a slope of zero.

Step-by-step explanation:

The student asked which of the following statements is true given the point (3, -4) on the graph:

• A) The line y = -4 is perpendicular to the y-axis and has an undefined slope.
• B) The line y = -4 is parallel to the y-axis and has a slope of zero.
• C) The line x = 3 is perpendicular with the x-axis and has an undefined slope.
• D) The line x = 3 is perpendicular to the y-axis and has a slope of zero.

The correct answer is B) The line y = -4 is parallel to the x-axis and has a slope of zero. A horizontal line like y = -4 does not rise or fall as it moves left or right, which is why its slope is zero. Option D is also true; the line x = 3 is perpendicular to the y-axis and because it is a vertical line, it has an undefined slope, not a slope of zero as stated.