Question

A recipe for a smoothie calls for 5 cups of strawberries for every 2 cups of bananas. The line represents the relationship between the amount of strawberries and the amount of bananas needed to make a smoothie according to the recipe. The point (1,2.5) is on the line. a. Label the axes appropriately. b. Write the equation that represents the proportional relationship between strawberries and bananas. Indicate the meaning of each variable. c. Explain the meaning of the point (1,2.5) in terms of the situation.

Answer 1

a)

x-axis= bananas

y-axis=strawberries

b) s=2.5b

c)the point (1,2.5) means that when you have 1 banana for the recipe you will need 2.5 strawberries to maintain the original recipe.

Explanation

Step 1

the point (1,2.5)

is

$\begin{gathered} x-\text{axis(horizontal)}=1 \\ y-\text{axis(vertical)}=2.5 \end{gathered}$

comparing the proportions

$\begin{gathered} \frac{2\text{ cups of bananas}}{5\text{ cups of strawberries}}=\frac{1}{2.5} \\ \\ \text{then} \end{gathered}$

x-axis is for the bananas

y-axis is for the strawberries

Step 2

Let

b represents the number of bananas for the recipe

s represents the number of strawberries for the recipe

Here, we have a line, and we know 2 points, we can find the equation of the line

a)find the slope using

$\begin{gathered} \text{slope}=m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}$

Let

P1(0,0) (for zero strawberries you need zero bananas)

P2(1,2.5)

b)replace

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{2.5-0}{1-0} \\ \text{slope}=\frac{2.5}{1}=2.5 \end{gathered}$

c)P1(0,0) m=2.5

find the equation using:

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{replacing} \\ y-0=2.5(x-0) \\ y=2.5x \end{gathered}$

in our variables

$s=2.5b$

it means the number of strawberries must be 2.5 times the number of bananas.

Step 3

the point (1,2.5) means that when you have 1 banana for the recipe you will need 2.5 strawberries to maintain the original recipe.

I hope this helps you