Answer :
find the equation of the line that pass through points (12,-1) and (4,-5)
find the slope of the line
[tex]\begin{gathered} m=\frac{_{}y_2-y_1_{}}{x_2-x_1} \\ m=\frac{-5-(-1)}{4-(12)} \\ m=\frac{-4}{-8} \\ m=\frac{1}{2} \end{gathered}[/tex]find the y intercept replacing one of the points
[tex]\begin{gathered} y=\frac{1}{2}x+b \\ -5=\frac{1}{2}(4)+b \\ -5=2+b \\ -5-2=b \\ -7=b \end{gathered}[/tex]write the complete equation
[tex]y=\frac{1}{2}x-7[/tex]replace the coordinate x of the points into the equation, if y is equal to the coordinate then the points lie on the same line.
when x=6
[tex]\begin{gathered} y=\frac{1}{2}(6)-7 \\ y=3-7 \\ y=-4 \end{gathered}[/tex]the point (6,-3) does not lie on the same line
when x=0
[tex]\begin{gathered} y=\frac{1}{2}(0)-7 \\ y=-7 \end{gathered}[/tex]the point (0,7) lies on the same line.
when x=-5
[tex]\begin{gathered} y=\frac{1}{2}(-5)-7 \\ y=-2.5-7 \\ y=-9.5 \end{gathered}[/tex]the point (-5,4) does not lie on the same line
when x=2
[tex]\begin{gathered} y=\frac{1}{2}(2)-7 \\ y=1-7 \\ y=-6 \end{gathered}[/tex]the point (2,-6) lies on the same line
when x=16
[tex]\begin{gathered} y=\frac{1}{2}(16)-7 \\ y=8-7 \\ y=1 \end{gathered}[/tex]the point (16,1) lies on the same line
when x=-4
[tex]\begin{gathered} y=\frac{1}{2}(-4)-7 \\ y=-2-7 \\ y=-9 \end{gathered}[/tex]the point (-4,5) does not lie on the same line.
The points that will lie on the same line will be (0,-7);(2,-6);(16,1)