Question

Which of the following is NOT true about the following equation? y=−3

A) It is the equation of a horizontal line.
B) Its slope is zero.
C) It is perpendicular to the equation y=13x+2.
D) The line does not cross the x-axis.

Answer 1

The statement which is NOT true about the equation y = -3 is

It is perpendicular to the equation y = 1/3x + 2 ⇒ C

Explanation:

Let us revise the facts of the horizontal line:

• The line is horizontal if all points on it have the same y-coordinates

• The horizontal line is parallel to the x-axis

• The slope of the horizontal line is zero

• The equation of the horizontal line is y = b, where b is the y-coordinate of all points on the line

• The y-intercept of the horizontal line is (0, b)

∵ The equation of the line is y = -3

→ Which means the value of y = -3 at any value of x

∴ The line is horizontal

∴ Its slope = 0

∵ The horizontal line is parallel to the x-axis

∴ The line does not intersect the x-axis

∴ The true statements are:

• It is the equation of a horizontal line

• Its slope is zero

• The line does not cross the x-axis

The statement which is NOT true about the equation y = -3 is

It is perpendicular to the equation y = 1/3x + 2