Direct Variation – Practice Problems

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When variables are related by a constant, they have a direct variation. This constant is designated as the k-value, and we can write this relationship as a formula: y = kx or k = y/x.

As always, using algebra, you can solve for the unknown value by isolating the variable, so if you know two values of the equation, you can solve for the third. When variables have a direct variation, as one variable increases so will the other variable, at the same rate. Likewise, as the one variable decreases so will the other variable, also at the same rate.

When you graph this relationship, you will notice the k-value determines the steepness of the line, just like the m-value in the slope-intercept form but with one major different. On the graphs of a line with a direct variation between the two values - the line always passes through the origin. If the line does not pass through the point ( 0, 0 ) then there is no direct variation and no constant of variation, k.

Understanding the topic of direct variation is especially important for real world use such as currency exchange. You wouldn’t want to get stranded in Tibet without enough Renminbi in your pocket just because you didn’t understand how to calculate the exchange rate with the dollar using the constant of variation. To see what I mean, watch this video.

Write equations of the line using slope.


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Exercises in this Practice Problem
Draw the graph that represents the described direct variation.
Determine the factor $k$.
Determine body weight on different planets.
Identify the equations.
Summarize the characteristics of direct variations.
Find the equations that are represented by the graphs.