Question

For each of the following exercises, y varies directly as x. find the value as indicated. 1) if y=6, when x = 3, find y when x = 9. 2) if y=10, when x=2, find y when x = 7. 3) if y=-20, when x = 5, find y when x = 3. 4) if y=4, when x = 8, find y when x = 21. 5) if y = 12, when x = 3, find x when y = 28.

Answer 1

To solve for y when y varies directly as x, first calculate the constant of variation k using given x and y values, and then apply it to find the new y values or x if required.

Step-by-step explanation:

When y varies directly as x, the relationship between y and x can be represented with the equation y = kx, where k is the constant of variation. To find the value of k, we use the given pairs of x and y.

1. For y=6 when x=3, we find k by dividing y by x. So, k = 6 / 3 = 2. Now, to find y when x=9, we multiply k by the new value of x: y = k * 9 = 2 * 9 = 18.
2. For y=10 when x=2, k = 10 / 2 = 5. To find y when x=7, y = 5 * 7 = 35.
3. For y=-20 when x=5, k = -20 / 5 = -4. To find y when x=3, y = -4 * 3 = -12.
4. For y=4 when x=8, k = 4 / 8 = 0.5. To find y when x=21, y = 0.5 * 21 = 10.5.
5. Lastly, for y=12 when x=3, k = 12 / 3 = 4. To find x when y=28, we rearrange the equation to x = y / k, so x = 28 / 4 = 7.