Question

(50 POINTS!) You buy a bottle of water and a dish of frozen yogurt. The table shows the total cost of the purchase

Answer 1

Given:

The objective is to find the linear model that represent the total cost given inthe table.

The general linear model for a straight line is,

`y=mx+c`

Here, x represents the ounces of frozen yogurt, y represents the total cost, m represents the slope of the linear model and c represents the y intercept.

Consider first two coordinates,

`\begin{gathered} (x_1,y_1)=(4,3.75) \\ (x_2,y_2)=(4.5,4) \end{gathered}`

The slope m can be calculated by,

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

Substitute the given values in the above equation.

`\begin{gathered} m=(4-3.75)/(4.5-4) \\ m=(0.25)/(0.5) \\ m=0.5 \end{gathered}`

Now, substitute the value of m, x, y in the equation of straight line to find y intercept.

`\begin{gathered} \text{3}.75=0.5(4)+c \\ \text{3}.75=2+c \\ c=3.75-2 \\ c=1.75 \end{gathered}`

Substitute the value of slope and y intercept in general equation, to obtain the required linear model.

`\begin{gathered} y=ms+c \\ y=0.5x+1.75 \end{gathered}`

Hence, the required linear model is obtained.