Two negative points will always be found in Quadrant III.

Although coordinate point  \(\displaystyle \small (4,1)\) has the largest \(\displaystyle \small x\) value in comparison to the other answer choices--it is the closest point to the \(\displaystyle \small x\)-axis becaues of the points \(\displaystyle \small y\) value.

Compare the absolute value of each of the coordinate points \(\displaystyle \small y\) values. Since, the absolute value of point \(\displaystyle \small (4,1)\) is the lowest, the point has the shortest distance to the \(\displaystyle \small x\)-axis.

 

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.