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. -2x+6y=-12
B. 3x-9y=9
C. x-3y=6
D. 9x-3y=6
To determine which equation results in a system of equations with exactly one solution, we need to find the equation that matches the given graph.
We can find the equation of a linear equation using the formula: y = mx + b, where m is the slope and b is the y-intercept.
Looking at the given points, we can calculate the slope by finding the change in y divided by the change in x.
First, let's calculate the slope between the points (negative 9, negative 5) and (negative 6, negative 4):
Slope = (y2 - y1) / (x2 - x1)
= (-4 - (-5)) / (-6 - (-9))
= (-4 + 5) / (-6 + 9)
= 1 / 3
Similarly, we can calculate the slope between the other points:
Slope between (negative 6, negative 4) and (negative 3, negative 3) = 1 / 3
Slope between (negative 3, negative 3) and (0, -2) = 1 / 3
Slope between (0, -2) and (3, -1) = 1 / 3
Slope between (3, -1) and (6, 0) = 1 / 3
Slope between (6, 0) and (9, 1) = 1 / 3
We can see that the slope between all the points is constant and equal to 1/3.
Now let's find the y-intercept by substituting the values of one of the points in the slope-intercept formula. Let's choose the point (0, -2):
-2 = (1/3)(0) + b
-2 = b
So the y-intercept is -2.
Therefore, the equation that matches the given graph is y = (1/3)x - 2.
To determine which equation results in a system of equations with exactly one solution, we need to check which equation has the same slope-intercept form.
A. -2x + 6y = -12 is not in slope-intercept form.
B. 3x - 9y = 9 is not in slope-intercept form.
C. x - 3y = 6 is not in slope-intercept form.
D. 9x - 3y = 6 is not in slope-intercept form.
Therefore, the equation that results in a system of equations with exactly one solution is not present among A, B, C, and D.