Determine which function has the greater rate of change in problems one through three
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To determine which function has the greater rate of change, we need to find the slope of each function. The slope represents how much the dependent variable (y) changes when the independent variable (x) changes by 1 unit.
1. Calculate the slope of the first function:
Take any two points on the graph of the first function and use the formula: slope = (change in y) / (change in x).
For example, if the function is y = 2x + 3, we can choose the points (1, 5) and (2, 7).
Slope = (7 - 5) / (2 - 1) = 2 / 1 = 2.
2. Calculate the slope of the second function:
Follow the same process as above, using different points from the graph of the second function.
For instance, if the function is y = 5x - 2, we can select the points (0, -2) and (1, 3).
Slope = (3 - (-2)) / (1 - 0) = 5 / 1 = 5.
3. Calculate the slope of the third function:
Again, choose different points on the graph of the third function and find the slope.
Let's say the function is y = -3x + 4, and we pick the points (-1, 7) and (0, 4).
Slope = (4 - 7) / (0 - (-1)) = -3 / 1 = -3.
Now, comparing the slopes obtained:
- The first function has a slope of 2.
- The second function has a slope of 5.
- The third function has a slope of -3.
From the given information, we can conclude that the second function (y = 5x - 2) has the greatest rate of change since it has the highest slope (5).