Question

according to the table, what was the rate of change between 2016 and 2017? students per year

Explanation:

Step1: Recall the formula for rate of change

The formula for rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(x\) represent the year and \(y\) represent the number of students. For 2016 (\(x_1 = 2016,y_1=19\)) and 2017 (\(x_2 = 2017,y_2 = 14\)).

Step2: Substitute values into the formula

Substitute \(x_1 = 2016,y_1=19,x_2 = 2017,y_2 = 14\) into \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We get \(m=\frac{14 - 19}{2017 - 2016}\).

Step3: Calculate the rate of change

First, calculate the numerator: \(14−19=-5\). Then calculate the denominator: \(2017 - 2016 = 1\). So \(m=\frac{-5}{1}=-5\).

Answer:

\(-5\)