Mathematics
OpenStudy (anonymous):

Help with one pre-calc question.

OpenStudy (anonymous):

If y varies directly as x, and y = 5 when x = 8, find y when x = 4

OpenStudy (anonymous):

@ganeshie8

OpenStudy (anonymous):

I think you can set that up as a proportion, so you'd have 5/8=y/4 and you'd solve that for y.

OpenStudy (anonymous):

Cross multiply?

OpenStudy (anonymous):

5/2?

OpenStudy (anonymous):

(5/2) is what I get, yeah

OpenStudy (jdoe0001):

something varies directly to "something else" means something = (some number) * "something else" y = n * x what's "n"? we dunno, but we know that when x = 8, y = 5 thus $$\bf y = n\cdot x\\ \quad \\ \quad \\ x =8\qquad y = 5\\ \quad \\ 5 = n\cdot 8$$ to find "n", that is, the "constant of variation", solve for "n"

OpenStudy (jdoe0001):

once you find the "constant of variation", you plug it back in the original function and, you want to know what "y" is when x = 4, well, just plug the "n" value and "x" value and get "y"

OpenStudy (anonymous):

n=5/8

OpenStudy (anonymous):

So y= 5/8 * 4

OpenStudy (jdoe0001):

$$\bf y = n\cdot x\\ \quad \\ \quad \\ x =8\qquad y = 5\\ \quad \\ 5 = n\cdot 8 \implies \cfrac{5}{8}=n\\ \quad \\ \textit{so what's "y" when x = 4?}\\ \quad \\ y = n\cdot x\implies y = \cfrac{5}{8} x\implies y = \cfrac{5}{8} \cdot 4 \implies y = \cfrac{20}{8}$$ yeap

OpenStudy (anonymous):

Or 5/2

OpenStudy (anonymous):

Thank you both.

OpenStudy (jdoe0001):

$$\bf y = \cfrac{\cancel{20}}{\cancel{8}}\implies\cfrac{5}{2}$$

OpenStudy (jdoe0001):

yw