Question

an international food festival charges for admission and for each sample of food. admission and 3 samples cost $5.75. admission and 7 samples cost $9.75. 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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(3,5.75)\) and \((x_2,y_2)=(7,9.75)\). Then \(m=\frac{9.75 - 5.75}{7 - 3}=\frac{4}{4}=1\).

Step2: Find the y - intercept

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 1\), \(x_1=3\), \(y_1 = 5.75\). \(y-5.75=1\times(x - 3)\), \(y-5.75=x - 3\), \(y=x+2.75\).

Answer:

\(y=x + 2.75\)