The rate of change for the given table is constant because the Line graph for the given values gives a straight line. Thus, the rate of change value for the given table is given by the slope formula for the obtained straight line. For a straight line, the ROC is always a constant. On calculating the constant rate of change is 19.
Rate of Change:
The rate of change describes how an output quantity changes relative to the change in input quantity.
To find the average rate of change, we divide the change in output quantity by the change in input quantity.
ROC=Change in output/Change in input
- For any given quantities, plotting a graph gives a linear or nonlinear function i.e., a straight line or a curve.
- If the graph shows a linear function or a straight line either it is increasing or decreasing, the rate of change remains constant i.e., it remains the same at all the intervals.
- If the graph shows a non-linear function or a curve then the rate of change is variable i.e., it varies at different intervals.
- ROC can be determined by calculating the slope of the straight line obtained in the graph
Calculating the rate of change for the given table:
Step 1:
The graph for the given table is shown below
The obtained graph is a straight line, so the rate of change is constant.
Step 2:
Calculating the slope which is the required rate of change
Slope (m) is given by the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking the middle intervals,
[tex]y_{2} =133\\y_1=76[/tex]
And
[tex]x_2=7\\x_1=4[/tex]
On substituting,
[tex]m=\frac{133-76}{7-4} \\=\frac{57}{3}\\ =19[/tex]
Thus, the rate of change for the values in the given table is 19.
Therefore, the rate of change for the given values remains constant as they form a straight line graph and the rate of change in the intervals between them is 19.
Learn more about the rate of change and slope of a line here:
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