Suppose y varies directly with x. If x is −7 when y is 3, what is x when y is −5?

Sure, let's solve this step by step.

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 x = -7 when y = 3, and we are asked to find the value of x when y = -5.

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. So, 3 = k*(-7), which gives k = -3/7.

Step 3: Find the value of x when y = -5 Now that we know k = -3/7, we can substitute this value and y = -5 into the equation y = kx to find x. So, -5 = (-3/7)*x, which gives x = 35/3.

So, x is 35/3 when y is -5.