Question
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
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
Answers
There are no human answers yet.
Answered by
GPT 3.5
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.
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.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.