Since the $\displaystyle \small y$-axis runs vertically, the point that has the $\displaystyle \small x$ coordinate with the lowest absolute value will be closest to the $\displaystyle \small y$-axis. Therefore, coordinate point $\displaystyle \small (-1,8)$ has the shortest distance to the $\displaystyle \small y$-axis, because the point is only a distance of $\displaystyle \small 1$ away from the $\displaystyle \small y$-axis. Every other coordinate point has an absolute distance of $\displaystyle \small 2$ or more. 

Compare the absolute value of each of the coordinate points $\displaystyle \small y$ values. Since, the $\displaystyle \small y$ value of point $\displaystyle \small \small (1.-7)$ has the greatest absolute value, this point has the farthest distance to the horizontal $\displaystyle \small x$-axis.

To find the equation of the line that passes through coordinate point $\displaystyle \small (6,4)$, plug the $\displaystyle \small x$ and $\displaystyle \small y$ values into each equation. The correct equation will end with a true statement. 

The solution is:
$\displaystyle \small x=6$, $\displaystyle \small y=4$


$\displaystyle \small y=\frac{3}{2}x-5$

$\displaystyle \small 4=\frac{3}{2}(6)-5$

$\displaystyle \small 4=\frac{18}{2}-5$

$\displaystyle \small 4=9-5$

$\displaystyle \small 4=4$

Since the $\displaystyle \small y$-axis runs vertically, the point that has the $\displaystyle \small x$ coordinate with the greatest absolute value will be farthest from the $\displaystyle \small y$-axis. Therefore, coordinate point $\displaystyle \small \small (8,-5)$ has the longest distance to the $\displaystyle \small y$-axis, because the point is a distance of $\displaystyle \small 8$ away from the $\displaystyle \small y$-axis. Every other coordinate point has an absolute distance of $\displaystyle \small \small 6$ or less. 

To find the equation of the line that passes through coordinate point $\displaystyle \small (4,8)$, plug the $\displaystyle \small x$ and $\displaystyle \small y$ values into each equation. The correct equation will end with a true statement. 

The solution is:
$\displaystyle \small x=4$,$\displaystyle \small y=8$

$\displaystyle \small y=2x$
$\displaystyle \small 8=2(4)$
$\displaystyle \small 8=8$

Recall that in a coordinate $\displaystyle (x, y)$, the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point $\displaystyle (2, 2)$, move $\displaystyle 2$ units to the right on the x-axis, then move $\displaystyle 2$ units up on the y-axis.

Recall that in a coordinate $\displaystyle (x, y)$, the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point $\displaystyle (-6, 2)$, move $\displaystyle 6$ units to the left on the x-axis, then move $\displaystyle 2$ units up on the y-axis.

Recall that in a coordinate $\displaystyle (x, y)$, the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point $\displaystyle (-12, -5)$, move $\displaystyle 12$ units to the left on the x-axis, then move $\displaystyle 5$ units down on the y-axis.

Recall that in a coordinate $\displaystyle (x, y)$, the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point $\displaystyle (-6, -6)$, move $\displaystyle 6$ units to the left on the x-axis, then move $\displaystyle 6$ units down on the y-axis.

Recall that in a coordinate $\displaystyle (x, y)$, the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point $\displaystyle (13, -7)$, move $\displaystyle 13$ units to the right on the x-axis, then move $\displaystyle 7$ units down on the y-axis.