A linear equation is graphed on the coordinate grid below.
The graph shows a coordinate grid with a straight line that passes through the points (negative 9, negative 5), (negative 6, negative 4) (negative 3, negative 3), (0, negative 2), (3, negative 1), (6, 0), and (9, 1).
When graphed on the same coordinate grid, which equation results in a system of equations with exactly one solution?
A.
B.
C.
D.
To determine which equation results in a system of equations with exactly one solution, we need to look for an equation that corresponds to a line that passes through two points that are not the same.
By looking at the given points, we can see that the line passes through the points (0, -2) and (9, 1).
To find the equation of the line passing through these two points, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope:
slope = (change in y) / (change in x)
slope = (1 - (-2)) / (9 - 0)
slope = 3/9
slope = 1/3
Now that we have the slope, we can use the point-slope form to find the equation:
y - y1 = m(x - x1), where (x1, y1) is one of the given points.
Using the point (0, -2):
y - (-2) = (1/3)(x - 0)
y + 2 = (1/3)x
Finally, we can rearrange the equation to slope-intercept form:
y = (1/3)x - 2
Therefore, the equation that results in a system of equations with exactly one solution is B.