Question

Since 2012, the price of a school lunch at Westown High School has risen at a constant rate.In 2014, the price of a school lunch was $2.25. The price rose to $3.20 by 2019.Complete the equation that describes the relationship between the price of a school lunch indollars, P, and the elapsed time in years since 2012, t.Write your answer using whole numbers or decimals rounded to the nearest hundredth.P=t +

Answer 1

$y=0.19x-380.41$

Explanation

Step 1

Let

P1(2014,2.25)

P2(2019,3.20)

a) find the rate of change( slope)

$\begin{gathered} \text{slope}=\frac{change\text{ in y }}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{replace} \\ \text{slope}=\frac{3.20-2.25}{2019-2014}=\frac{0.95}{5}=0.19 \end{gathered}$

bI find the equation of the line

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{replace} \\ y-2.25=0.19(x-2014) \\ y-2.25=0.19x-382.66 \\ \text{add 2.25 in both sides} \\ y-2.25+2.25=0.19x-382.66+2.25 \\ y=0.19x-380.41 \end{gathered}$

I hope this helps you