Question

Which equation represents the price y to have x custom t-shirts shipped?The table shows the cost ofcustom t-shirts, including aone-time shipping fee.Number of custom5 10 15 20t-shirts, xPrice ($), y55 105 155 205Ay=50x + 5y = 10x + 5y = 503y = 10.2

Answer 1

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:

`y(x)=m\cdot x+b`

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:

`m=(y_2-y_1)/(x_2-x_1)`

Where (x1, y1) and (x2, y2) are points that belong to the line. We will choose the points (5, 55) and (10, 105).

`m=(105-55)/(10-5)=(50)/(5)=10`

To find b we need to replace one known point on the first expression.

`\begin{gathered} 55=10\cdot5+b \\ b=55-10\cdot5 \\ b=55-50=5 \end{gathered}`

The expression is:

`y(x)=10\cdot x+5`

The correct answer is the third one.