Question

for items 5 and 6, identify the constant of proportionality.
5.

x	y
5	30
7	42

6.

x	y
6	4.5
8	6

for items 7 and 8, write an equation that models the proportional relationship.
7.

x	y
5	-20
7	-28

8.

x	y
5	\\(\frac{15}{2}\\)
6	9

Explanation:

Item 5

Step1: Recall the formula for constant of proportionality ($k$) in a proportional relationship $y = kx$, so $k=\frac{y}{x}$.

Step2: Calculate $k$ for the first pair ($x = 3$, $y = 18$): $k=\frac{18}{3}=6$.

Step3: Verify with the second pair ($x = 5$, $y = 30$): $\frac{30}{5}=6$.

Step4: Verify with the third pair ($x = 7$, $y = 42$): $\frac{42}{7}=6$.

Step1: Use $k=\frac{y}{x}$ for the proportional relationship $y = kx$.

Step2: Calculate $k$ for the first pair ($x = 4$, $y = 3$): $k=\frac{3}{4}=0.75$.

Step3: Verify with the second pair ($x = 6$, $y = 4.5$): $\frac{4.5}{6}=0.75$.

Step4: Verify with the third pair ($x = 8$, $y = 6$): $\frac{6}{8}=0.75$.

Step1: Find the constant of proportionality $k$ using $k=\frac{y}{x}$.

Step2: For ($x = 3$, $y = - 12$): $k=\frac{-12}{3}=-4$.

Step3: The equation for a proportional relationship is $y = kx$, so substitute $k=-4$.

Answer:

6

Item 6