if y varies directly as x and y= 3 when x = 10, find x when y=8

Answer 1

Hi, Emily,

If x varies directly with y, we have a linear equation and can assume it has the form y = mx + b. As x changes up or down, y will follow, at a rate determined by m, the slope. b is the y-intercept, or where the line crosses the y axis at x = 0. The problem simply states "varies directly," and I don't see enough information to calculate a value for b, so let's simplify the formula to y = mx. Change x and y will respond directly, either up or down. We just don't know how quickly y will change, since we don't know m, yet.

We are given one point that fits this line, (10,3). We can use that to determine m by plugging in the values for the equation and find m:

3 = m(10)

m = (3/10)

y = (3/10)x

The next question is what is x when y = 8,.

8 = (3/10)x

x = (80/3), or 26.67

Seems like an odd number, but it's what I conclude.

I hope this helps (and that I'm correct),

Bob

Answer 2

y varies directly as x means y=kx.

Using y=3 and x=10 you can find k.

3=k 10

k=3/10 therefore y=3/10 x

Now replace y=8 above and find x.