Mai measured the height, perimeter, and area of some equilateral triangles. Her measurements are shown in the tables.

1. Could the relationship between the triangles’ heights and their perimeters be proportional? Explain your reasoning.

   height (cm)	perimeter (cm)
   1.1	3.9
   2.4	8.1
   4.1	14.4
   5.5	19.2
   7.9	27.3

2. Could the relationship between the triangles’ heights and their areas be proportional? Explain your reasoning.

   height (cm)	area (cm2)
   1.1	0.715
   2.4	3.24
   4.1	9.84
   5.5	17.6
   7.9	35.945

Diego made a graph of two quantities that he measured and said, “The points all lie on a line except one, which is a little bit above the line. This means that the quantities can’t be proportional.” Do you agree with Diego? Explain.

For each graph, explain whether the relationship could be proportional.

Graph of 7 plotted points, origin O, with grid. Horizontal axis, number of bricks, scale 0 to 21, by 3’s. Vertical axis, height of triangular wall in inches, scale 0 to 15, by 3’s. Points plotted at 0 comma 0, 1 comma 2.25, 3 comma 4.5, 6 comma 6.75, 10 comma 9, 15 comma 11.25, 21 comma 13.5.

Graph of 7 plotted points, origin O, with grid. Horizontal axis, number of coins, scale 0 to 18, by 3’s. Vertical axis, weight of coins in grams, scale 0 to 50, by 10’s. Points plotted at 0 comma 0, 3 comma 7, 6 comma 20, 9 comma 29, 12 comma 36, 15 comma 47, 18 comma 56.

The graph shows that while it was being filled, the amount of water in gallons in a swimming pool was approximately proportional to the time that has passed in minutes.

1. About how much water was in the pool after 25 minutes?
2. Approximately when were there 500 gallons of water in the pool?
3. Estimate the constant of proportionality for the gallons of water per minute going into the pool.

Graph of 5 plotted points, origin O, with grid. Horizontal axis, time, minutes, scale 0 to 50, by 10’s. Vertical axis, water, gallons, scale 0 to 700, by 100’s. Plotted points at approximately 10 comma 150, 20 comma 305, 30 comma 420, 40 comma 600, 50 comma 720.