1. If y = 12 when x = 4, then we can set up the proportion: y/x = 12/4. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = 12/4 = 3. To find y when x = 12, we can substitute x = 12 into the equation y = 3x to get: y = 3(12) = 36.
2. If y = -18 when x = 9, then we can set up the proportion: y/x = -18/9. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = -18/9 = -2. To find y when x = 7, we can substitute x = 7 into the equation y = -2x to get: y = -2(7) = -14.
3. If y = -3 when x = -4, then we can set up the proportion: y/x = -3/-4. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = -3/-4 = 3/4. To find x when y = 2, we can substitute y = 2 into the equation y = (3/4)x to get: 2 = (3/4)x. Solving for x, we get: x = 8/3.
4. If y = 3 when x = 10, then we can set up the proportion: y/x = 3/10. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = 3/10 = 3/10. To find x when y = 1.2, we can substitute y = 1.2 into the equation y = (3/10)x to get: 1.2 = (3/10)x. Solving for x, we get: x = 12.
5. If y = 2.5 when x = .25, then we can set up the proportion: y/x = 2.5/.25. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = 2.5/.25 = 10. To find y when x = .75, we can substitute x = .75 into the equation y = 10x to get: y = 10(.75) = 7.5.
Answers & Comments
Answer:
1. If y = 12 when x = 4, then we can set up the proportion: y/x = 12/4. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = 12/4 = 3. To find y when x = 12, we can substitute x = 12 into the equation y = 3x to get: y = 3(12) = 36.
2. If y = -18 when x = 9, then we can set up the proportion: y/x = -18/9. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = -18/9 = -2. To find y when x = 7, we can substitute x = 7 into the equation y = -2x to get: y = -2(7) = -14.
3. If y = -3 when x = -4, then we can set up the proportion: y/x = -3/-4. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = -3/-4 = 3/4. To find x when y = 2, we can substitute y = 2 into the equation y = (3/4)x to get: 2 = (3/4)x. Solving for x, we get: x = 8/3.
4. If y = 3 when x = 10, then we can set up the proportion: y/x = 3/10. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = 3/10 = 3/10. To find x when y = 1.2, we can substitute y = 1.2 into the equation y = (3/10)x to get: 1.2 = (3/10)x. Solving for x, we get: x = 12.
5. If y = 2.5 when x = .25, then we can set up the proportion: y/x = 2.5/.25. Since y varies directly as x, we can say that y is directly proportional to x, or y = kx for some constant k. In this case, k = 2.5/.25 = 10. To find y when x = .75, we can substitute x = .75 into the equation y = 10x to get: y = 10(.75) = 7.5.
Step-by-step explanation: