How to solve direct linear variation / proportion worded problems (with examples)

Two examples are shown that involve quantities that vary directly with each other.

In solving these direct variation problems, the first step is to write down the variation equation in the form y = kx.

The second step is to determine the value of k, which is the constant of variation (also called the constant of proportionality).

Note that linear models generally have limitations and are not perfect representations of reality, and it is important to think about what these limitations and/or imperfections may be depending on the context.

for example, if we are talking about a mass on a spring, and the stretch of the spring varies directly with the size of the mass attached, then one limitation is there is a limit on the size of mass that can be attached before the spring is permanently stretched or damaged.