Question

A friend gave Ms. Morris a gift card for a local car wash. The table shows the linear relationship of how the value left on the card relates to the number of car washes. Number of car washes, X Amount left on card (S), 0 50 8 30 12 20 Part 1 out of 3 Enter an equation that shows the number of dollars left on the card. The equation that represents this situation is y = Check Nec

Answer 1

Answer:

y = -2.5x + 50

Explanations:

Considering the values on the table:

`\begin{gathered} x_1=0,x_2=8,x_3=12 \\ y_1=50,y_2=30,y_3=20 \end{gathered}`

Since the question has already said there is a linear relationship between the value left on the card (y) and the number of car washes (x), there will be a constant slope(m) on the graph

`\begin{gathered} m\text{ = }(y_2-y_1)/(x_2-x_1) \\ m\text{ = }(30-50)/(8-0) \\ m\text{ = }(-20)/(8) \\ m\text{ = -2.5} \end{gathered}`

The equation of a line having a slope, m, and passing through the point

(x₁, y₁) is given as:

`\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 50= -2.5(x - 0)} \\ y\text{ - 50 = -2.5x} \\ y\text{ = -2.5x + 50} \end{gathered}`

The equation that shows the number of dollars left on the card is:

y = -2.5x + 50