For the direct variation y = (3/4) when x = (1/8), how do you find the constant of variation and find the value of y when x = 3?

Question

For the direct variation y = (3/4) when x = (1/8), how do you find the constant of variation and find the value of y when x = 3?

1 Answer

Impact of this question

7378 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-21T18:40:13

For direct variation $y = \frac{3}{4}$ $y=3/4$ when $x = \frac{1}{8}$ $x=1/8$ the constant of variation is $k = 6$ $k=6$ , and when $x = 3$ $x=3$ we have $y = 18$ $y=18$ .

Explanation:

If a variable y varies directly with a variable x, then y is proportional to x.

The statement y is proportional to x, is the same as y equals x times a constant k.

$y \propto x \Leftrightarrow y = k x$ $y prop x <=> y=kx$

Then we can plug in the case we already know if $y = \frac{3}{4}$ $y=3/4$ then $x = \frac{1}{8}$ $x=1/8$ .

$\Rightarrow \frac{3}{4} = k \frac{1}{8}$ $=> 3/4=k1/8$ So we need to solve for k

$\Leftrightarrow 8 (\frac{3}{4}) = \frac{24}{4} = 6 = k$ $<=> 8(3/4)=24/4=6=k$ Multiply both sides by 8 and simplify

So, $k = 6$ $k=6$

Then we have $y = 6 x$ $y=6x$

so we plug in $x = 3$ $x=3$

$y = 6 (3) = 18$ $y=6(3)=18$

Science

Math

Humanities

... and beyond

For the direct variation y = (3/4) when x = (1/8), how do you find the constant of variation and find the value of y when x = 3?

1 Answer

Explanation:

Related questions

Impact of this question