a. The constant of proportionality is 21.
b. An equation that relates the width of a row of townhouses and the number of townhouses is y = 21x.
c. The width of 9 townhouses is 189 feet.
In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:
y = kx
Where:
- y represents the y-variable or width.
- x represents the x-variable or number of townhouses.
- k is the constant of proportionality.
Part a.
Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 105/5
Constant of proportionality, k = 21
Part b.
Therefore, the required linear equation for the relationship between y and x is given by;
y = kx
y = 21x.
Part c.
The width of 9 townhouses in feet is given by;
y = 21 × 9
y = 189 feet.
Complete Question:
5. The width of a row of identical townhouses, y, and the number of townhouses, x, have a proportional relationship. The width of 5 townhouses is 105 ft.
a. What is the constant of proportionality?
b. Write an equation that relates the width of a row of townhouses and the number of townhouses.
c. What would be the width of 9 townhouses in feet?