If y varies directly with x and y=–90 when x=9, find x when y=–80.Write and solve a direct variation equation to find the answer.

Sure, here are the steps to solve the problem:

Step 1: Understand the problem The problem states that y varies directly with x. This means that y = kx for some constant k. We are given that y = -90 when x = 9, and we are asked to find x when y = -80.

Step 2: Find the constant of variation We can find the constant of variation k by substituting the given values of x and y into the equation y = kx. This gives -90 = k*9. Solving for k, we get k = -90/9 = -10.

Step 3: Substitute the constant of variation into the equation Now that we know k = -10, we can substitute this into the equation y = kx to get y = -10x.

Step 4: Solve for x We are asked to find x when y = -80. Substituting y = -80 into the equation y = -10x gives -80 = -10x. Solving for x, we get x = -80/-10 = 8.

So, when y = -80, x = 8.