Question

1. determine if the table is proportional, if it is, state the constant of proportionality. lemons 3 4 5 6 cups of sugar $1\frac{1}{2}$ 2 $2\frac{1}{2}$ 3 \bigcirc yes, k=1/2 \bigcirc yes, k=2 \bigcirc yes, k=3 \bigcirc no

Explanation:

Step1: Define proportionality check

A table is proportional if $\frac{\text{Cups of Sugar}}{\text{Lemons}} = k$ (constant) for all pairs.

Step2: Calculate ratio for first pair

$\frac{1\frac{1}{2}}{3} = \frac{\frac{3}{2}}{3} = \frac{3}{2} \times \frac{1}{3} = \frac{1}{2}$

Step3: Calculate ratio for second pair

$\frac{2}{4} = \frac{1}{2}$

Step4: Calculate ratio for third pair

$\frac{2\frac{1}{2}}{5} = \frac{\frac{5}{2}}{5} = \frac{5}{2} \times \frac{1}{5} = \frac{1}{2}$

Step5: Calculate ratio for fourth pair

$\frac{3}{6} = \frac{1}{2}$

Step6: Verify constant ratio

All ratios equal $\frac{1}{2}$, so $k=\frac{1}{2}$.

Answer:

yes, k=1/2