Question 388262

A change in one quantity with respect to another quantity is called a
{{{rate}}}{{{ of}}}{{{ change}}} . 

Any rate of change can be described in terms of slope, or {{{change_in_y/change_in_x}}}.

A special type of equation that describes a rate of change is a
linear equation in the form of {{{y =kx}}}, where {{{k}}} is {{{not}}} equal to {{{0}}}, and is called {{{direct}}} {{{variation}}}. 

In direct variation we say that {{{y}}} varies {{{directly}}} with {{{x}}} or {{{y}}} varies directly as {{{x}}}. 

In the direct variation equation, {{{y =kx}}}, {{{k}}} is the
{{{constant}}} of variation. 

The constant of variation in a direct variation equation has the {{{same}}}{{{ value}}} as the {{{slope}}} of the graph. 

For example:
{{{y =3x}}} is a direct variation because it is in the form of {{{y =kx}}}. 

The constant of variation of {{{y =3x}}} is {{{3}}}. 

The slope of the linear graph of {{{y=3x}}} is {{{3}}}. All direct variation graphs pass through the {{{origin}}}.


So, in your case we have:{{{y =7x}}}. The constant of variation it is {{{7}}}.

If the value of {{{y}}} is {{{12}}}, then the value of {{{x}}} would be {{{x=y/7}}} or {{{x=12/7}}}.

{{{x=1.7}}}