A linear equation is graphed on the coordinate grid below.

To determine which equation results in a system of equations with exactly one solution, we need to find the equation of the graphed line.

First, we can find the slope of the line using the two points (-9, -5) and (9, 1).

The slope is given by: slope = (change in y) / (change in x)

Slope = (1 - (-5)) / (9 - (-9))
Slope = 6 / 18
Slope = 1/3

Next, we can use the point-slope form of a linear equation to find the equation of the line using the point (-9, -5):

y - y1 = m(x - x1)

y - (-5) = (1/3)(x - (-9))
y + 5 = (1/3)(x + 9)
3(y + 5) = x + 9
3y + 15 = x + 9
3y - x = -6

So, the equation of the line is 3y - x = -6.

Now, let's check which equation results in a system of equations with exactly one solution:

A. -2x + 6y = -12
B. 3x - 9y = 9
C. x - 3y = 6
D. 9x - 3y = 6

Plug in the values of x and y from one of the given points into each equation:

For (-9, -5):
A. -2(-9) + 6(-5) = -12
B. 3(-9) - 9(-5) = 9
C. (-9) - 3(-5) = 6
D. 9(-9) - 3(-5) = 6

Looking at the answers, we see that only equation C results in the same value on both sides of the equation when (-9, -5) is plugged in:

(-9) - 3(-5) = 6

Therefore, the equation that results in a system of equations with exactly one solution is C. x - 3y = 6.