To determine which of these functions has a greater rate of change than the given line, we need to compare the slopes (rate of change) of the functions.
The slope of a line can be calculated using the formula: slope = (change in y) / (change in x).
Looking at the graphed line, it passes through the points (-4.5, -12) and (4.5, 12). The change in y is 12 - (-12) = 24, and the change in x is 4.5 - (-4.5) = 9. Thus, the slope of the graphed line is 24/9 = 8/3 ≈ 2.67.
A. y = 2x + 12 has a slope of 2, which is less than the slope of the graphed line (2.67). Therefore, it does not have a greater rate of change.
B. y = 2x + 12 has a slope of 2, which is less than the slope of the graphed line (2.67). Therefore, it does not have a greater rate of change.
C. y = 10x + 1 has a slope of 10, which is greater than the slope of the graphed line (2.67). Therefore, it has a greater rate of change.
D. y = 10x + 1 has a slope of 10, which is greater than the slope of the graphed line (2.67). Therefore, it has a greater rate of change.
Therefore, the correct answer is either C or D, as both have a greater rate of change than the given graph.
Which of these functions has a greater rate of change than the function graphed below, and why?
On the coordinate plane, two points are at (-4.5, -12) and (4.5, 12) are connected through a line.
A.
y = 2x + 12, because the rate of change of the graphed function is 3
B.
y = 2x + 12, because the rate of change of the graphed function is 9
C.
y = 10x + 1, because the rate of change of the graphed function is 3
D.
y = 10x + 1, because the rate of change of the graphed function is 9
1 answer
1 answer