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?

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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?

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Answer 1 · 2017-11-11T14:09:46

$y = 5 x$ $y=5x$

Explanation:

$given y \propto x$ $"given "ypropx$

$then y = k x \leftarrow equation for direct variation$ $"then "y=kxlarrcolor(blue)"equation for direct variation"$

$where k is the constant of variation$ $"where k is the constant of variation"$

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

$y = k x \Rightarrow k = \frac{y}{x} = \frac{10}{2} = 5$ $y=kxrArrk=y/x=10/2=5$

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

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

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

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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?

1 Answer

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