Question

What is an equation of the direct variation that includes the point `(-10, -17)`?

Answer 1

`y=17/10x`

Explanation:

`"the equation of 2 quantities in direct variation is"`

`•color(white)(x)y=kxlarrcolor(blue)"k is constant of variation"`

`"to find k use the given point "(-10,-17)`

`"that is "x=-10,y=-17`

`y=kxrArrk=y/x=(-17)/(-10)=17/10`

`"equation is " color(red)(bar(ul(|color(white)color(black)(y=17/10x)color(white)(2/2)|)))`

Answer 2

`17x-10y=0`

Explanation:

A direct variation will always go through the point `(0,0)`

Given that it also goes through `(-10,-17)`

We could write the slope equations
`color(white)("XXX")(y-0)/(x-0)=(0-(-17))/(0-(-10))=17/10`
or
`color(white)("XXX")y/x=17/10`
or
`color(white)("XXX")10y=17x`
or (in standard form)
`color(white)("XXX")17x-10y=0`