How can a table be used to find the rate of change and the initial value? Describe the process.
+605 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.
