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
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the given line is
[tex]m=\dfrac{-2-(-2)}{4-1}=\dfrac{0}{3}=0.[/tex]
Since the line passes through the point (1, -2), so its equation will be
[tex]y-(-2)=m(x-1)\\\\\Rightarrow y+2=0(x-1)\\\\\Rightarrow y+2=0\\\\\Rightarrow y=-2.[/tex]
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
