The price of purchase can be represented as a function of the numbers of shirts bought in a way that the function is linear. This means that it increases at a constant rate. A linear function has the following form:
[tex]y(x)=m\cdot x+b[/tex]Where m is the rate of change and b is the y-intercept. The rate of change on our case is the price of the shirt and the y-intercept is the one time fee. To determine the value of m we can use the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are points that belong to the line. We will choose the points (5, 55) and (10, 105).
[tex]m=\frac{105-55}{10-5}=\frac{50}{5}=10[/tex]To find b we need to replace one known point on the first expression.
[tex]\begin{gathered} 55=10\cdot5+b \\ b=55-10\cdot5 \\ b=55-50=5 \end{gathered}[/tex]The expression is:
[tex]y(x)=10\cdot x+5[/tex]The correct answer is the third one.
