The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y  and solve for x:

2x - 3(1) = 5

2x - 3 = 5

2x = 8

x = 4. So the missing x-value on line l is 4.

Test the difference combinations out starting with the most repeated number.  In this case, y = 7 appears most often in the answers.  Plug in y=7 and solve for x.  If the answer does not appear on the list, solve for the next most common coordinate.

2(x) + 9(7) = 71

2x + 63 = 71

2x = 8

x = 4

Therefore the answer is (4, 7)

In order to find out which of these lines is correct, we simply plug in the values $\displaystyle \dpi{100} \small x=8$ and $\displaystyle \dpi{100} \small y=9$ into each equation and see if it balances.

The only one for which this will work is $\displaystyle \dpi{100} \small 3x-6=2y$

$\displaystyle \dpi{100} \small 5x+25y = 125$

Test the coordinates to find the ordered pair that makes the equation of the line true:

$\displaystyle \dpi{100} \small (5,4)$

$\displaystyle \dpi{100} \small 5 (5) + 25 (4) = 25 + 100 = 125$

$\displaystyle \dpi{100} \small (1,5)$

$\displaystyle \dpi{100} \small 5(1)+25(5)= 5+125=130$

$\displaystyle \dpi{100} \small (5,1)$

$\displaystyle \dpi{100} \small 5(5)+25(1)= 25+25=50$

$\displaystyle \dpi{100} \small (5,5)$

$\displaystyle \dpi{100} \small 5(5)+25(5)= 25+125=150$

$\displaystyle \dpi{100} \small (1,4)$

$\displaystyle \dpi{100} \small 5(1)+25(4)= 5+100=105$

Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:

Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.

To test the coordinates, plug the x-coordinate into the line equation and solve for y.

y = 1/3x -7

Test (3,-6)

y = 1/3(3) – 7 = 1 – 7 = -6   YES!

Test (3,7)

y = 1/3(3) – 7 = 1 – 7 = -6  NO

Test (6,-12)

y = 1/3(6) – 7 = 2 – 7 = -5  NO

Test (6,5)

y = 1/3(6) – 7 = 2 – 7 = -5  NO

Test (9,5)

y = 1/3(9) – 7 = 3 – 7 = -4  NO

Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2.  Then we substitute y = 2 into one of the original equations to get x = –2.  So the solution to the system of equations is (–2, 2)

$\displaystyle (2,2)$ when plugged in for $\displaystyle y$ and $\displaystyle x$ make the linear equation true, therefore those coordinates fall on that line.

$\displaystyle y=3x-4$

$\displaystyle 2=3(2)-4$

$\displaystyle 2=6-4$

$\displaystyle 2=2$

Because this equation is true, the point must lie on the line. The other given answer choices do not result in true equalities.

We are looking for an ordered pair that makes the given equation true. To solve, plug in the various answer choices to find the true equality.

$\displaystyle y=3x+2$

$\displaystyle 5=3(1)+2$

$\displaystyle 5=3+2$

$\displaystyle 5=5$

Because this equality is true, we can conclude that the point $\displaystyle (1,5)$ lies on this line. None of the other given answer options will result in a true equality.

To figure out if any of the points are on the line, substitute the $\displaystyle x$ and $\displaystyle y$ coordinates into the equation. If the equation is incorrect, the point is not on the line. For the point $\displaystyle (4,12.5)$:

$\displaystyle 12.5\neq \frac{5}{2}(4)+3$

$\displaystyle 12.5\neq 13$

So, $\displaystyle (4,12.5)$ is not on the line.