Question

What can be concluded about a line that passes through the points (1, -2) and (4, -2) Check all that apply.

The slope is 0.
The y-intercept is -2.
The line is vertical.
The line is horizontal.
The line has no y-intercept.
The equation of the line is y = -2

Answer 1

The first one the second one the fourth one and the last one

Answer 2

Answer: The correct options are

(A) The slope is 0.

(B) The y-intercept is -2.

(C) The line is horizontal.

(D) The equation of the line is y = -2

Step-by-step explanation: We are given to select the statements that can be concluded about a line that passes through the points (1, -2) and (4, -2).

We know that

the slope of a line passing through the points (a, b) and (c, d) is given by

`m=(d-b)/(c-a).`

So, the slope of the given line is

`m=(-2-(-2))/(4-1)=(0)/(3)=0.`

Since the line passes through the point (1, -2), so its equation will be

`y-(-2)=m(x-1)\\\\\Rightarrow y+2=0(x-1)\\\\\Rightarrow y+2=0\\\\\Rightarrow y=-2.`

Comparing with the slope-intercept form y=mx+c, we get

y-intercept, c = -2.

Also, the line is of the form y = a, which is parallel to the x axis, so the given line is horizontal.

Thus, the correct options are

(A) The slope is 0.

(B) The y-intercept is -2.

(C) The line is horizontal.

(D) The equation of the line is y = -2