Question

The graph shows the number of servings in different amounts of frozen yogurt listed on a carton. Enter anequation that gives the number of servings y inx pints. Use only decimal form, if necessary.

Answer 1

We have been given a graph that shows numbers of servings (y) in different amounts (x) of frozen yogurt listed on a carton.

To write an equation that gives the number of servings y in x pints, we will have to find the slope (rate of change) of our given linear function.

Since we know that rate of change of a function can be found by vertical change of the function divided by horizontal change of the function.

We pick any two point in the graph given, consider the image below

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \\ \text{Where } \\ x_1=2,x_2=4 \\ y_1=5,y_2=10 \end{gathered}`

Substitute into the formula and obtain the slope

`\begin{gathered} \text{Slope =}\frac{\text{10-5}}{4-2}=(5)/(2)=2.5 \\ \text{Hence } \\ \text{Slope}=2.5 \end{gathered}`

Hence the equation is of the form

`\begin{gathered} y=mx\text{ +c} \\ \text{where m=slope and c=intercept on y} \\ \end{gathered}`

since

m=2.5 and c=0,

The equation that gives the number of servings y in x pints is y=2.5x