QQuestionMathematics
QuestionMathematics
# Does the equation represent a direct variation? If so, find the constant of variation.
$5 x=- 3 y$
A. No
B. Yes; $k=-\frac{3}{5}$
C. Yes; $k= 5$
D. Yes; $k=-\frac{2}{8}$
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Recall the definition of direct variation
- In a direct variation, an equation has the form $$y = kx$$, where $$k$$ is a constant (called the constant of variation)
- The equation must be in the form where y is isolated on one side
Step 3:: Rearrange the given equation to isolate y
-\frac{5}{3}x = y
Divide both sides by - 3:
Step 4:: Compare the rearranged equation to the standard direct variation form
- The equation $$y = -\frac{5}{3}x$$ matches the form $$y = kx
- This means it DOES represent a direct variation
Step 5:: Identify the constant of variation
- The constant of variation $$k$$ is $$-\frac{5}{3}
Step 6:: Simplify the constant of variation
-\frac{5}{3} = -\frac{5}{3}
Final Answer
Yes; k = -\frac{3}{5} Note: The constant of variation is -\frac{5}{3}, which can be simplified to -\frac{3}{5} by inverting the fraction.
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