Question

Please Help!! The graph of the line y = 4 is a A) vertical line with a slope of zero. B) horizontal line with a slope of zero. Eliminate C) vertical line with an undefined slope. D) horizontal line with an undefined slope.

Answer 1

The answer is D that a horizontal line with an undefined slope. This is because the coordinate is (0,4)

Answer 2

B) horizontal line with a slope of zero.

Explanation:

∵ The equation of the type y = mx + c is always a straight line having the slope m,

Also,
`m=\tan\theta`

Where,

`\theta` = angle from the positive x-axis,

If m = 0, ⇒
`\tan \theta=0\implies \theta =0`

i.e. line is parallel to x-axis or a horizontal line,

if m = ∞ ⇒
`\tan \theta = \infty\implies \cos\theta = 0\implies \theta = 90^(\circ)`

i.e. line is perpendicular to x-axis or vertical,

Here, the given line,

y = 4,

⇒ y = 0x + 4

By comparing,

m = 0,

⇒ It is a horizontal line with a slope of zero.

Hence, OPTION B is correct.