Practice with Direct Variation Topic Index | Algebra Index | Regents Exam Prep Center

 Try the following:
 1. If m varies directly as y and m is 6 when y is 36, find the constant of variation. Choose: 1/6 6 1/36 36 Explanation If m varies directly as y, m/y = k. 6/36 = k 1/6 = k

 2. "a varies directly as b".  If a = 3 when b = 24, find b when a = 10. Choose: 1.25 8 36 80 Explanation If a varies directly as b,  a/b = k. 3/24 = 10/b 3b = 240 b = 80

 3. There are about 200 calories in 50 grams of Swiss cheese.  Willie ate 70 grams of this cheese.  About how many calories were in the cheese that he ate if the number of calories varies directly as the weight of the cheese. Choose: 210 240 280 290 Explanation The calories varies directly as the grams, c/g = k. 200/50 = c/70 50c = 14000 c = 280 calories

4. In the following chart, does one variable vary directly with the other?
 M 3 4 5 6 7 N 6 8 10 12 14

Choose:

Yes
No

5. In the following chart, does one variable vary directly with the other?
 X 1 2 3 4 5 Y 1 4 9 12 15

Choose:

Yes
No

6. One variable (A) varies directly as the other (C).  Find the missing numbers x and y.  Write the formula which relates the variables.
 A 1 2 x C 3 y 15

Choose:

x = 3 and y = 6
x = 13 and y = 4
x = 5 and y = 6
x = 4 and y = 9

 7. The resistance (R) of a copper wire, varies directly as its length (L).  Write this relation as a formula using k as the constant of variation. Explanation R = kL R/L = k

 8. A salesman's commission varies directly as his sales.  Write the formula relating this situation and denote the variables.  If the commission is \$100 for \$1000 in sales, find the commission for \$1750 in sales. Choose: \$125 \$150 \$175 \$200 Explanation c = commission and s = sales. c = ks    and      c/s = k 100/1000 = x/1750 1000x = 175000 x = 175

 9. The distance an object, a, drops from rest in freefall varies directly with the square of the time, t.  If a varies directly as t2, and a = 12 when t = 2, find a when t = 3. Choose: 6 9 27 81 Explanation If a varies directly as t², then a = kt². 12 = k • 4 so k = 3 a = 3 • 3² = 3 • 9 = 27

 10. Which equation represents:       x varies directly as y,                    and       x = 12 when y = 36? Choose: Explanation Remember: y varies directly as x is represented by y = kx. This question asks for the reverse order.

 11. Which graph represents a direct variation? Choose: Explanation In direct variation, as x increases, y increases.

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Michael Caldwell