We are given that a line passes through the points (1, -2) and (4, -2)
Recall that the equation of the line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope of the line is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex][tex]\text{where}(x_1,y_1)=(1,-2)\text{and}(x_2,y_2)=(4,-2)[/tex]Let us substitute the given values into the slope formula
[tex]m=\frac{-2-(-2)}{4-1}=-\frac{-2+2}{3}=\frac{0}{3}=0[/tex]So the slope is 0 (check option 1)
Now let us find the y-intercept (b)
Choose any one point from the given two points
Let choose (1, -2) and substitute it into the slope-intercept equation
[tex]\begin{gathered} y=mx+b \\ -2=0\cdot1+b \\ -2=0+b \\ b=-2 \end{gathered}[/tex]So the y-intercept is -2 (check option 2)
The equation of the line becomes
[tex]\begin{gathered} y=mx+b \\ y=0\cdot x-2 \\ y=0-2 \\ y=-2 \end{gathered}[/tex]So the equation of the line is y = -2 (check option 6)
Also note that horizontal lines have 0 slope.
Since the slope is 0, it is a horizontal line (check option 4)
Conclusion:
Options 1, 2, 4 and 6 are correct.
