Name: ______Date: ______Hour: ______
Introduction to Direct Proportions vs. Inverse Proportions
Direct proportion: As one variable increases, the other variable also increases. When you graph them it forms a line with positive slope.
Inverse Proportion: As one variable increases, the other variable decreases. When you graph them it forms a decreasing curve.
As you solve the following puzzles, try to decide if the numbers they make form a direct proportion, an inverse proportion, or some other relationship.
1. I’m thinking of two numbers. If you take half of the 1st number, you get the 2nd number.
a. Fill in the table with 6 possible solutions to this puzzle. Make some solutions positive and some negative.
x / yb. Graph your solutions. Connect the points.
c. What shape is your graph?
d. Write an equation that matches this puzzle. Solve this equation for y.
e. Is this a direct proportion, an inverse proportion, or neither? Explain.
2. I’m thinking of two numbers. If you multiply the numbers, you get 12.
a. Fill in the table with 5 possible solutions to this puzzle. Make some solutions positive and some negative.
x / yb. Graph your solutions. Connect the points.
c. What shape is your graph?
d. Write an equation that matches this puzzle. Solve this equation for y.
e. Is this a direct proportion, an inverse proportion, or neither? Explain.
3. I’m thinking of two numbers. If you multiply the 1st number by 3 and then divide by 2, you get the 2nd number.
a. Fill in the table with 5 possible solutions to this puzzle. Make some solutions positive and some negative.
x / yb. Graph your solutions. Connect the points.
c. What shape is your graph?
d. Write an equation that matches this puzzle. Solve this equation for y.
e. Is this a direct proportion, an inverse proportion, or neither? Explain.
4. I’m thinking of two numbers. If you divide 24 by the 1st number, you get the 2nd number.
a. Fill in the table with 5 possible solutions to this puzzle. Make some solutions positive and some negative.
x / yb. Graph your solutions. Connect the points.
c. What shape is your graph?
d. Write an equation that matches this puzzle. Solve this equation for y.
e. Is this a direct proportion, an inverse proportion, or neither? Explain.
5. Summary: Half of your equations should have been direct proportions and the other half inverse proportions.
a. Compare the graphs of direct proportions vs. inverse proportions. How can you easily tell which is which by looking at their shape?
b. Compare the equations of direct proportions vs. inverse proportions. How can you easily tell which is which by looking at the equations?
6. You stretch a slingshot back 2 inches to shoot a rock. You measure how far the rock travels. Then you stretch the slingshot back more and more and see how far the same rock travels. Will the relationship between Stretch amount and distance be a direct proportion or an inverse proportion? Why?
7. You stretch a slingshot back 2 inches to shoot a rock. You measure how far the rock travels. Then you find heavier & heavier rocks, but keep the same stretch and see how far the new rock travels. Will the relationship between Rock Weight and distance be a direct proportion or an inverse proportion? Why?