Start by calculating the change between each pair of consecutive x and y.
Yes
Practice makes perfect
For a function defined in terms of x and y, the rate of change of the function is a ratio that compares the change in y to change in x. We want to determine if the rate of change of the points given in the table is constant. Let's start by recalling the formula for the rate of change.
Rate of change=Change inx/Change inyNow, we will calculate the changes between consecutive x and y terms.
Change in $x$:& 2+3 → 5+3 → 8+3 →11
Change in $y$:& 6+9 →15+9 →24+9 →33
As we can see, the change between each pair of consecutive x is 3 and the change between each pair of consecutive y equals 9. Therefore for each pair of consecutive points we can calculate the rate of change by substituting 3 for change inx and 9 for change iny into the formula.
Rate of change=9/3=3
Since the changes in x and y are constant, the rate of change is also constant. We found that its value is 3.
Extra
Constant Rate of Change
If the rate of change is constant, then the function is linear and its rate of change is referred to as the slope of the line. That is why we often want to know if the rate of change is constant — it tells us whether a function is linear.
