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 in dollars, P, and the elapsed time in years since 2012,
Write your answer using whole numbers or decimals rounded to the nearest hundredth.

Please help I don’t understand

  P = 0.14t +2.25

Step-by-step explanation:

The statement that "the price of a school lunch ... has risen at a constant rate" is telling you that the price can be modeled by a linear equation. If P is the price, and t is years after 2012, you are given two points on the line:

  (t, P) = (0, 2.25) and (7, 3.20)

You can use these points to find the equation of the line in the usual way.

  m = (y2 -y1)/(x2 -x1) . . . . . . slope of a line through (x1, y1) and (x2, y2)

  m = (3.20 -2.25)/(7 -0) = 0.95/7 ≈ 0.14

The first point tells you the equation intercept, so the relationship between P and t is ...

  y = mx +b . . . . . . . m = slope; b = y-intercept. We're using (t, P) for (x, y).

  P = 0.14t +2.25

a² + b²= c²

24² + 7² = c²

c= 25