What are the plots for graphing? How do I graph this equation?

Question

Chloe is buying souvenirs on vacation. She wants to spend $70 at the most but only has 60 cubic inches of space available in her luggage.

if bracelets cost $7 and take up 3 in3 of space and t-shirts are $5 but take 15 in3 of space, write and graph a system of four inequalities thatmodel Chloe's possible purchases. letx= number of bracelets and y= number of t-shirts; use a scale of 2 on both axes.

I understand how to do this, I just am very confused on the graphing

thank you

Answer 1

You are creating a space on the graph that contains all the possible combinations of purchases possible as described in the problem. The axes of the graph represent the number of bracelets (x axis) and t-shirts (y axis) that can be purchased and fit into the luggage.

Two of the four inequalities you need to graph are are implicit, x>0 and y>0, which are the axes of the graph. These simply mean that you cannot buy a negative number of either item. The other two are the inequalities for cost and volume. You graph those as well. For cost you graph the line 7x + 5y = 70 and shade the region below the line. Do the same for volume with 3x + 15y = 60 and shade below that line. The scaling by 2 means that you increment your axes by 2s: 2, 4, 6, 8, ...