To determine wich coordinates points match up with the equations you have to replace said equations with the x-coordinate and see if the result is equal to the y-coordinate.
First point (0,0)
x=0 and y=0
1st equation
[tex]y=13x+5[/tex]Replace it with x=0
[tex]\begin{gathered} y=13\cdot0+5 \\ y=5 \end{gathered}[/tex]This point doesn't match up with this equation.
2nd equation
[tex]y=-3x[/tex]Replace with x=0
[tex]\begin{gathered} y=-3\cdot0 \\ y=0 \end{gathered}[/tex]This point matches up with the equation.
3rd equation
[tex]y=x-10[/tex]Replace with x=0
[tex]\begin{gathered} y=0-10 \\ y=-10 \end{gathered}[/tex]This point doesn't match up with this equation.
Result, the point (0,0), called origin, matches up with the equation in the second column.
Second point (8,-2)
x=8 y=-2
First equation
[tex]y=13x+5[/tex]Replace with x=8
[tex]\begin{gathered} y=13\cdot8+5 \\ y=109 \end{gathered}[/tex]This point doesn't match up with this equation.
Second equation
[tex]y=-3x[/tex]Replace with x=8
[tex]\begin{gathered} y=-3\cdot8 \\ y=-24 \end{gathered}[/tex]This point doesn't match up with this equation.
Third equation
[tex]y=x-10[/tex]Replace with x=8
[tex]\begin{gathered} y=8-10 \\ y=-2 \end{gathered}[/tex]This point matches up with the equation.
Result, the point (8,-2), matches up with the equation in the third column.