Question

doghhouse dollars
two companies, barkly and woofington, both sell doghouses. the cost of each doghouse depends on the size of its base.
use the table and the blank graph below for exercises 1 - 4.
1 barkly doghouses charges $50 per square meter for its doghouses. complete the table to show this proportional relationship.
size (m²) 0.5 1 2.5 4
cost ($) 25 50 125 200
2 graph the proportional relationship.
3 write an equation to show the relationship in your table and graph. use x for size and y for cost.
y = 50x
4 woofington doghouses charges half as much per square meter as barkly. draw the graph for woofington on the axes above. label both graphs with their equations. is the price per square meter charged by woofington also a proportional relationship? explain your reasoning.
yes because it goes in a straight line and passes the origin.

Explanation:

Step1: Analyze Woofington's rate

Since Woofington charges half as much per square - meter as Barkly, and Barkly charges $50 per square - meter, Woofington charges $25 per square - meter.

Step2: Write Woofington's equation

If $x$ is the size in square meters and $y$ is the cost, the equation for Woofington is $y = 25x$.

Step3: Determine proportionality

A proportional relationship has the form $y=kx$ where $k$ is a non - zero constant and the graph is a straight line passing through the origin $(0,0)$. For $y = 25x$, it is of the form $y=kx$ with $k = 25$, and its graph is a straight line passing through the origin. So it is a proportional relationship.

Answer:

The equation for Woofington is $y = 25x$, and the price per square meter charged by Woofington is a proportional relationship because its equation is of the form $y=kx$ (where $k = 25$) and its graph is a straight line passing through the origin.