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need help on this test

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How can a table be used to find the rate of change and the initial value? Describe the process.

Feb 25, 2021

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Let's take this table:

 x 0 1 2 3 y 1 3 5 7

The initial value is the first value, i.e. $x=0$ and $y=1$.

The rate of change (for linear functions) is the difference between the $y$ values when the $x$ value changes by $1$. Looking closely, as $x$ goes up by $1$, $y$ goes up by $2$. The rate of change is $\frac{\text{change in y}}{\text{change in x}}=\frac{2}{1}=\boxed{2}$.

Hope this helped.

Feb 25, 2021