Question

If y varies directly with x, write an equation for the direct variation. Then find each value.

a). If y = –5 when x = 2, find y when x = 8.

Answer 1

The equation for direct variation is y = kx, where k is the constant of variation. By substituting the given values of y and x into the equation, we can find the value of k. Then, we can use k to find the value of y when x = 8.

Step-by-step explanation:

The given problem states that y varies directly with x. When two variables vary directly, their relationship can be represented by the equation y = kx, where k is the constant of variation. We need to find the equation for direct variation and then find the value of y when x = 8.

To find k, we can substitute the given values of y and x into the equation. When y = -5 and x = 2, we have -5 = k(2). Solving for k, we get k = -2.5.

Now that we have the value of k, we can use it to find y when x = 8. Substituting k = -2.5 and x = 8 into the equation, we get y = -2.5(8) = -20.