Question

(1) Is the slope of the line having y=5 as its equation zero or undefined?

(2) is the slope of the line having x=-4 as it’s equation zero or undefined?

Answer choices: (A)the slope is neither zero or undefined. (B) the slope is undefined. (C) the slope is zero

Answer 1

(1) The slope of the line having y = 5 as its equation is zero ⇒ (C)

(2) The slope of the line having x = -4 as its equation is undefined ⇒ (B)

Explanation:

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

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

• The slope of the horizontal line is zero

• The line is a vertical line if the x-coordinates of all points lie on it have the same value

• The equation of the vertical line is x = a, a is the x-intercept (a, 0)

• The slope of the vertical line is undefined

Let us use the rules above to solve the question

(1)

∵ The equation of the line is y = 5

→ That means the line is horizontal

∴ The line is a horizontal line

∵ The slope of the horizontal line = zero

∴ The slope of the line having y = 5 as its equation is zero

(2)

∵ The equation of the line is x = -4

→ That means the line is vertical

∴ The line is a vertical line

∵ The slope of the vertical line is undefined

∴ The slope of the line having x = -4 as its equation is undefined