What are some examples of linear equations in everyday life?

Answer 1

A linear equation is an equation that can be written in the form: y=mx+b.

An equation in this form can be graphed on a x/y coordinate plane, and the slope (m) can NOT be a vertical line, additionally it must pass the vertical line test; if a vertical line is drawn, no more than one y point may correspond to any one x point on the graph. The slope produced must be a line, so it must follow that the change in y is constant to the change in x.

Filling up a bath tub w/ water. The amount of water in the tub (graphed along the y-axis) and the amount of time that passes (graphed on x-axis) is constant. Slope (m) is stated to be the volume over time, which would be let's say 5 gallons per minute (y axis / x axis) (rise over run)

Walking a constant speed to school. Distance is y axis, time is x axis. Slope would be distance over time. If you move 2 meters per second, for 2 minutes (120 seconds) then this would produce a linear equation.

MANY examples in everyday life can be graphed as a linear function, but the important qualification is that whatever corresponds to the y axis, such as volume or distance, is constant relative to your x axis, most commonly time (seconds, minutes, hours).

However, in both my examples it's only linear if the change in volume/distance is CONSTANT over the change in time. So, if you fill up the bathtub for 2 minutes, turn it off, then turn it back on, this is not linear. Same goes for walking to school, if you walk at 2 meters per second, then speed up to 4 meters per second, then slow down to 1 meters per second, this is NOT a linear equation or linear graph because the change in y over the change in x is not constant anymore, it's variable.