Question

When Deven makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup. Here is a table that shows how to make batches of different sizes.
milk surpy 2 3
8 12
1 3/2
10 15
1.1) Are cups of milk and tablespoons of chocolate syrup in a proportional relationship? Response area
1.2) What is the scale factor from the first row to the second row in the table? Response area
1.3) What is a constant of proportionality for this relationship? Response area
Where can you see this constant of proportionality in the table? Response area

Answer 1

Step-by-step explanation:

Answer:

Part a) The table shows a proportional relationship between tablespoons of chocolate syrup and cups of milk

Part b) The scale factor is 1.5

Part c) The constant of proportionally for this relationship is 1.5

Part d) The units for the constant of proportionality are tablespoons of chocolate syrup per cups of milk

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line

Let

x ----> the quantity of cups of milk

y ----> the quantity of tablespoons of chocolate syrup

k ---> the constant of proportionality

For y=3, x=2 -----> k=\frac{y}{x}=\frac{3}{2}=1.5k=

x

y

=

2

3

=1.5

For y=12, x=8 -----> k=\frac{y}{x}=\frac{12}{8}=1.5k=

x

y

=

8

12

=1.5

For y=3/2, x=1 -----> k=\frac{y}{x}=\frac{(3/2)}{1}=1.5k=

x

y

=

1

(3/2)

=1.5

For y=15, x=10 -----> k=\frac{y}{x}=\frac{15}{10}=1.5k=

x

y

=

10

15

=1.5

therefore

The table shows a proportional relationship between tablespoons of chocolate syrup and cups of milk

The linear equation is

y=1.5xy=1.5x

That means----> The the quantity of tablespoons of chocolate syrup is 1.5 times the quantity of cups of milk

The scale factor is equal to the ratio between tablespoons of chocolate syrup and cups of milk. Is equal to the constant of proportionality k

The scale factor is 1.5

The constant of proportionality is 1.5

The units for the constant of proportionality are tablespoons of chocolate syrup per cups of milk

\frac{tablespoons\ of\ chocolate\ syrup}{cups\ of\ milk}

cups of milk

tablespoons of chocolate syrup