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,
[tex]y=mx+c[/tex]
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,
[tex]\begin{gathered} (x_1,y_1)=(4,3.75) \\ (x_2,y_2)=(4.5,4) \end{gathered}[/tex]
The slope m can be calculated by,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given values in the above equation.
[tex]\begin{gathered} m=\frac{4-3.75}{4.5-4} \\ m=\frac{0.25}{0.5} \\ m=0.5 \end{gathered}[/tex]
Now, substitute the value of m, x, y in the equation of straight line to find y intercept.
[tex]\begin{gathered} \text{3}.75=0.5(4)+c \\ \text{3}.75=2+c \\ c=3.75-2 \\ c=1.75 \end{gathered}[/tex]
Substitute the value of slope and y intercept in general equation, to obtain the required linear model.
[tex]\begin{gathered} y=ms+c \\ y=0.5x+1.75 \end{gathered}[/tex]
Hence, the required linear model is obtained.
