Question

Given that y varies directly with x, and x = 6, y = 102, how do you write a direct variation equation that relates x and y?

Answer 1

The equation that relates x & y is

`color(purple)(x/y = 1 / 17)`

Explanation:

Given `x color(white)(xx) alpha color(white)(xx) y`

Also `x = 6, y = 102`

`x : y = 6 : 102`

`x / y = (cancel(6) color(red)1) / (cancel(102) color(red)17) = 1/17`

The equation that relates x & y is

`color(purple)(x/y = 1 / 17)`

When x = 1, y = 17, when x = 2, y = 34, x = 6, y = 102 & so on.

Answer 2

`y=17x`

Explanation:

`"the initial statement is "ypropx`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`rArry=kx`

`"to find k use the given condition"`

`x=6" when "y=102`

`y=kxrArrk=y/x=102/6=17`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=17x)color(white)(2/2)|)))`