Question

The ordered pair (2, 10), is a solution of a direct variation, how do you write the equation of direct variation, then graph your equation and show that the slope of the line is equal to the constant of variation?

Answer 1

`y=5x`

Explanation:

`"given "ypropx`

`"then "y=kxlarrcolor(blue)"equation for direct variation"`

`"where k is the constant of variation"`

`"to find k use the given coordinate point "(2,10)`

`y=kxrArrk=y/x=10/2=5`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=5x)color(white)(2/2)|)))`

`y=5x" has the form "y=mxlarrcolor(blue)"m is the slope"`

`rArry=5x" is a straight line passing through the origin"`
`"with slope m = 5"`
graph{5x [-10, 10, -5, 5]}