in direct variation, as one number increases, so does the other. this is also called direct proportion.
y∝x —> y = kx
(∝ means directly proportional to)
here are some word problems that mean the same thing as y∝x:
"y is a simple multiple of x"
"y is directly proportional to x"
"y varies directly as x"
"y = kx"
example problems:
y∝x. When x = 5, y = 3. Find x when y = 20
y∝x --> y = kx
x = 5, y = 3 --> 3 = k * 5
3 = 5k
k= $$\frac{3}{5}$$
now that you know k, plug it into the original equation with y becoming 20
20 = $$\frac{3}{5}$$x
20 * 5 = $$\frac{3}{5* 5}$$x
100 = 3x
x = $$\frac{100}{3}$$
final answer is when y = 20, then x = $$33\frac{1}{3}$$
in inverse variation as one number increases, the other decreases. this is also known as indirect proportion.
y∝$$\frac{1}{x}$$ —> y = $$\frac{k}{x}$$
example question:
y is inversely proportional to x. when x = 3 then y = 6. find the value of y when x = 8.
y∝$$\frac{1}{x}$$ —> y = $$\frac{k}{x}$$
6 = $$\frac{k}{3}$$
k = 18
then fit it into original equation but when x = 8
y = $$\frac{18}{8}$$
y = $$\frac{9}{4}$$
final answer is when x = 8 then y = $$\frac{9}{4}$$