Question

an international food festival charges for admission and for each sample of food. admission and 4 samples cost $6.25. admission and 9 samples cost $11.25. write a linear function rule to model the cost y for any number of samples x. the linear function rule is y = □.

Explanation:

Step1: Find the slope (cost per sample)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(4,6.25)\) and \((x_2,y_2)=(9,11.25)\).
\(m=\frac{11.25 - 6.25}{9 - 4}=\frac{5}{5}=1\)

Step2: Find the y - intercept (admission cost)

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 1\), \(x_1=4\), \(y_1 = 6.25\)
\(y-6.25=1\times(x - 4)\)
\(y-6.25=x - 4\)
\(y=x+2.25\)

Answer:

\(y=x + 2.25\)