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?
To have exactly one solution, the equation must correspond to a line that intersects the given line at only one point.
Looking at the given points, we can see that the slope of the line is positive. This means that the equation of the line must also have a positive slope.
Let's calculate the slope of the given line:
slope = change in y / change in x = (1 - (-5)) / (9 -(-9)) = 6 / 18 = 1/3.
Therefore, the equation of the line must have a slope of 1/3 to have exactly one solution.
Now, let's check the options:
- y = -3x + 4 : This line has a slope of -3, so it does not have the same slope as the given line.
- y = -1/3x : This line has a slope of -1/3, so it does not have the same slope as the given line.
- y = 1/3x - 2 : This line has a slope of 1/3, which matches the slope of the given line.
- x + y = -2 : This is a linear equation in standard form. We can rewrite it as y = -x - 2, which has a slope of -1. Therefore, it does not have the same slope as the given line.
Therefore, the equation "y = 1/3x - 2" results in a system of equations with exactly one solution when graphed on the same coordinate grid.