Mikayla needs to order a countertop for her project. Company A will sell Mikayla a countertop according to the given graph, which includes a $1,000 installation fee. Company B will sell a countertop according to the values given in the table, which includes an $800 installation fee and a constant rate of change.

1. Which company charges a higher rate per square foot of countertop? How do you know?
A. Company A
B. Company B

2. Write a linear equation that represents the cost in dollars, $ y $, as a function of the amount of countertop needed in square feet, $ x $, for Company A.

3. Write a linear equation that represents the cost in dollars, $ y $, as a function of the amount of countertop needed in square feet, $ x $, for Company B.

4. At what number of square feet of countertop would the cost from each company be the same?

5. To keep costs low, Mikayla should hire _____ for this project, which requires 26 square feet of countertop.
A. Company A
B. Company B

Once we have the rate per square foot for both companies, we can create linear equations to represent the relationship between cost and countertop coverage for each company. Whichever company has a higher rate will charge more per square foot. We can also find where costs would be equal by finding the intersection point of the lines, and decide the best company for Mikayla's 26 square foot requirement.

Explanation:

Based on the information provided in your question, I can't answer your question completely because the actual values in the graphs and table representing the relationship between the cost and counter top coverage for companies A and B are not specified. However, once we have these values, we can construct two linear equations, one for each company, to compare their rates.

For Company A, the equation would look something like this: y = μx + $1,000 where y is the total cost, x is the countertop square footage, and μ is the rate per square foot.

For Company B, the equation would be much the same: y = mx + $800, where m is the rate per square foot.

Whichever company has a higher value for their rate per square foot (the coefficients μ and m) will charge more per square foot. We could also find the point of intersection between these two lines by setting the two equations equal to each other and solving for x. This will tell us at what amount of square footage the cost from each company would be the same. Given the area of 26 square feet Mikayla needs, you can substitute this value into the two equations and decide the cheaper option for her based on which company gives a lower cost.

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