Determine whether y varies directly with x. If so, find the constant of variation k and write the...


Determine whether {eq}y {/eq} varies directly with {eq}x {/eq}. If so, find the constant of variation {eq}k {/eq} and write the equation.

x y
7 11
8 13
9 15
10 17

Direct Variation

Direct variation in two variables is seen when both increase together or both decrease together. An example is the more electricity is consumed, the higher the bill is.

Answer and Explanation:

The direct variation will be seen if both the variables move in the same direction. So, if x increases in value, so does y and if x decreases in value, so does y.

If we look at the table given, we can see that y is increasing as x increases. So, the two are directly proportional to each other. This can be written as:

$$y=kx $$

Now, when x=7, y=11. So,

$$\begin{align} 7&=11k\\ \therefore k&=\frac{7}{11} \end{align} $$

Learn more about this topic:

Directly Proportional: Definition, Equation & Examples

from High School Algebra II: Help and Review

Chapter 1 / Lesson 23

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