Complete this sentence with the correct choice: y = 4 is a horizontal line with ________.

undefined slope.

a slope of 4.

a slope of 0.

None of the above will make a true statement.

Think this through...

If y=4, then x can be any number, but y will always be 4. Slope is defined as (the change in y)divided by (the change in x). If y doesn't change, that means your numerator will be 0.

Can you figure out the answer now?

Using the point-slope equation, find the equation containing (2, 5) and slope m = -3

Yes, the correct choice to complete the sentence is "a slope of 0."

If y = 4, it means that the y-coordinate is constant at 4, regardless of any changes in the x-coordinate. In other words, for every point on the line y = 4, the y-value remains constant at 4. Since the slope represents the change in y divided by the change in x, and there is no change in the y-coordinate, the slope is 0. Thus, a horizontal line has a slope of 0.