Question

vThe total cost of purchasing x cups of coffee at each of two competing coffee shops is represented by the graph and by the equation shown below.







image.png



Which statements accurately compare costs for the two coffee shops? Choose the TWO correct responses.


The price of a cup of coffee at each shop is the same.


Coffee Shop A has the most expensive coffee.


For 8 cups of coffee sold, the total cost at either coffee shop is $20.


Coffee Shop B has the most expensive coffee.


For 10 cups of coffee sold, the total cost at Coffee Shop A is $2.50 more than the total cost at Coffee Shop B.

Answer 1

I don't have the graph or the equation you mentioned. Could you upload the image or type the equation here?

Meanwhile, here's how to decide which TWO statements are true once I can see the graph/equation:

1. Write each shop's total-cost as a linear function: A(x) = m_A x + b_A and B(x) = m_B x + b_B.
- The slope m (rise/run on the graph) is the price per cup.
- The y-intercept b is any fixed fee.

2. Check each statement:
- "The price of a cup of coffee at each shop is the same." → True if and only if m_A = m_B.
- "Coffee Shop A/B has the most expensive coffee." → Compare slopes: whichever m is larger has the higher per-cup price.
- "For 8 cups..., total cost at either shop is $20." → True if A(8) = B(8) = 20.
- "For 10 cups..., A is $2.50 more than B." → True if A(10) − B(10) = 2.50.

3. To find where costs are equal (if needed), solve m_A x + b_A = m_B x + b_B, so x = (b_B − b_A)/(m_A − m_B) (when m_A ≠ m_B). Then plug that x into either function to get the common cost.

Post the graph or the equation and I’ll compute the slopes/intercepts and pick the two correct statements.