Question

mrs. scott told students how many rounds to expect in the spelling bee based on previous years.
rounds in the spelling bee
year rounds
2011 13
2012 6
2013 9
2014 9
2015 11
according to the table, what was the rate of change between 2011 and 2015?
rounds per year

Explanation:

Step1: Identify the formula for rate of change

The formula for rate of change (slope) is $\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points. Here, $x$ represents the year and $y$ represents the number of rounds. For 2011 ($x_1 = 2011$, $y_1=13$) and 2015 ($x_2 = 2015$, $y_2 = 11$).

Step2: Substitute the values into the formula

Substitute $x_1 = 2011$, $y_1 = 13$, $x_2=2015$, $y_2 = 11$ into $\frac{y_2 - y_1}{x_2 - x_1}$. We get $\frac{11 - 13}{2015 - 2011}=\frac{- 2}{4}$.

Step3: Simplify the fraction

Simplify $\frac{-2}{4}$. Divide both the numerator and the denominator by 2. $\frac{-2\div2}{4\div2}=-\frac{1}{2}=- 0.5$.

Answer:

$-0.5$