Question

1. determine if the graph is proportional, if it is, state the constant of proportionality.

options:
yes, k=1/10
no
yes, k=10
yes, k=20

Explanation:

Step1: Check proportionality condition

A proportional graph passes through the origin \((0,0)\) and has a constant ratio of \(y/x\) for all non-zero points. The given graph includes \((0,0)\), so we test other points.

Step2: Calculate ratio for point (1,10)

$\frac{\text{Total Cost}}{\text{Number of Tickets}} = \frac{10}{1} = 10$

Step3: Verify ratio for point (2,20)

$\frac{20}{2} = 10$

Step4: Verify ratio for point (3,30)

$\frac{30}{3} = 10$

Step5: Verify ratio for point (4,40)

$\frac{40}{4} = 10$
All ratios are equal, so the graph is proportional with constant \(k=10\).

Answer:

yes, k=10