Which rule matches the function graphed below?
A coordinate grid with both the x- and y-axes between negative 12 and 12, and each interval mark on the axes represents two units. A line is graphed that connects the points left-parenthesis negative 4 comma 8 right-parenthesis, left-parenthesis negative 2 comma 4 right-parenthesis, and left-parenthesis 0 comma 0 right-parenthesis.
A. y = –2x
B. y = x + 4
C. y = 2x
D. y = x – 4
B. y = x + 4
To determine which rule matches the function graphed, we can examine the slope of the line.
The slope of a line can be determined by finding the change in y divided by the change in x.
Let's find the slope using the given points: (-4, 8), (-2, 4), and (0, 0).
The change in x from (-4, 8) to (-2, 4) is 2, and the change in y is -4. Therefore, the slope is -4/2 = -2.
Now, let's check the choices:
A. y = -2x: The slope is indeed -2, so this could be a match.
B. y = x + 4: The slope is 1, so this does not match.
C. y = 2x: The slope is 2, so this does not match.
D. y = x - 4: The slope is 1, so this does not match.
Based on the slope, the rule that matches the function graphed is A. y = -2x.