Question

Let y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x. If y = –7 when x = –2, and y = 5 when x = 1, express y in terms of x. Show your work.

Answer 1

y = 3x + 2/x

Step-by-step explanation:

In this case, y is the difference between two numbers, say, a and b. So y = a – b. One number varies directly as x while the other varies inversely as x. as x, a= k1x. The equation we'll be using is y = k1x – k2/x.

If y = -7, x = 2, then -7 = -2k1 + k2/2

If y = 5, x = 1, then 5 = k1 – k2

We express y in terms of x with the following equation: y = 3x + 2/x

Answer 2

Let a and b the two numbers. So y = a – b. one number varies directly as x , a= k1x. while the other number varies inversely as x, b = k2/x. so the equation y = k1x – k2/x

At y = -7, x =2 then -7 = -2k1 + k2/2

At y = 5, x =1 then 5 = k1 – k2

Solving k1 and k2, 3 and -2 respectively

So y = 3x+2/x