ACT Preparation / Unit 9 ACT 0817 worked example, 60 to 90 seconds
Interpreting a Linear Model
The idea
A question about a linear model is answered in three steps. First, identify the input and the output and their units. Second, read the slope as the change in output per one unit of input, and the intercept as the output when the input is zero. Third, answer in the language of the situation, and check that a zero input makes sense there.
In practice
Worked example: a water tank's level is L = 800 − 25t, in liters, t minutes after a valve opens. The slope, −25, means the level falls 25 liters each minute. The intercept, 800, is the level at the moment the valve opens. When is it empty? 800 − 25t = 0, so t = 32 minutes: the t-intercept is the time the tank runs dry.
Where people slip
If the input cannot be zero in the situation, the intercept is only where the line starts, not a fact about the situation.
Your place on the trail
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