16. Graphs of equations with three variables

Raphael is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $2.00, and a bowl of salad costs $4.00. Let E be the amount in dollars that Raphael spends on pizza and salad. If Raphael buys P slices of pizza and S bowls of salad, then the total amount of money he spends (B) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Raphael has $32.00 to spend on pizza and salad; that is, E = $32.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Raphael can purchase with $32.00, when the number of pizza slices he purchases is 0. Budget Pizza Salad (Dollars) (Slices) (Bowls) 32.00 32.00 32.00 0Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Raphael can purchase with a budget of $32.00. 24 + Initial Budget O New Budget SALAD (Bowls) 2 6 8 10 12 14 16 18 20 22 24 PIZZA (Slices) Now suppose Raphael's income is cut in half : That is, he has 50% less money to spend than he did before. On the previous graph, use the blue line (circle symbols) to plot Raphael's new budget constraint. Which of the following statements best summarizes the pattern of causality captured by the graph above? Check all that apply. A change in P causes a change in S. The relationship between P and S is not a causal relationship. A change in S causes a change in P. A change in E causes a shift of the budget constraint