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.

a. The value of the constant k is 21

b. The equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.

Step-by-step explanation:

a.

A proportional relationship satisfies the equation y = k * x, where k is a positive constant and is called a proportionality constant. In this case "x" is the number of terraced houses and "y" is the width of a row of identical houses.

The data you have is that the width of 5 townhouses are 105 feet. This means that the value of "x" is 5 houses and the value of "y" is 105 feet. By replacing in the equation y = k * x and isolating the constant k, you get:

105=k*5

k=21

So the value of the constant k is 21.

b.

As mentioned, the equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.

This means that just as "x" increases, "y" increases. And that if "x" decreases, "y" will decrease. And this relationship between "x" e "and" will always be the same, determined by the value of the constant "k".

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.