Question

slope as rate of change
let’s practice!
1.)
the ratio of green marbles to blue marbles is 3:1 for a given pouch full of marbles. fill in the ratio table below with equivalent ratios that could reflect the number of blue marbles and green marbles that are contained in the pouch.

of blue marbles

of green marbles

the rate of change (slope) is

Explanation:

Step1: Confirm ratio relationship

The ratio of green to blue marbles is $3:1$, so $\text{Green marbles} = 3 \times \text{Blue marbles}$.

Step2: Verify table values

For blue marbles = 1: $\text{Green} = 3 \times 1 = 3$
For blue marbles = 2: $\text{Green} = 3 \times 2 = 6$
For blue marbles = 3: $\text{Green} = 3 \times 3 = 9$
For blue marbles = 4: $\text{Green} = 3 \times 4 = 12$

Step3: Calculate slope (rate of change)

Slope = $\frac{\text{Change in green marbles}}{\text{Change in blue marbles}} = \frac{3-0}{1-0} = 3$

Answer:

Completed ratio table:

# of blue marbles	1	2	3	4

The rate of change (slope) is $\boldsymbol{3}$