Question

refer to the data in the table to answer the following questions.
enter the constant of proportionality of the number of houses with monsters to the number of houses.
write an equation that shows the relationship between the two quantities using the variables provided in the table and the constant of proportionality.

	total number of houses (h)	number of houses with monsters (m)
b	119	49
c	158	56
d	179	70

Explanation:

Step1: Recall constant - of - proportionality formula

The constant of proportionality $k$ between two quantities $y$ (number of houses with monsters) and $x$ (total number of houses) is given by $k=\frac{y}{x}$.

Step2: Calculate for each row

For row A: $k_A=\frac{14}{34}=\frac{7}{17}\approx0.412$.
For row B: $k_B = \frac{48}{119}\approx0.403$.
For row C: $k_C=\frac{56}{136}=\frac{7}{17}\approx0.412$.
For row D: $k_D=\frac{70}{170}=\frac{7}{17}\approx0.412$.
The constant of proportionality $k = \frac{7}{17}$.

Step3: Write the proportion

If $m$ is the number of houses with monsters and $h$ is the total number of houses, the proportion is $m=\frac{7}{17}h$.

Answer:

Constant of proportionality: $\frac{7}{17}$
Proportion: $m=\frac{7}{17}h$