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A linear model

A linear model has a fixed addition per unit and a starting value. The starting value is the cost when x is zero, and the slope is how much y increases when x increases by 1. Between two points the slope is the difference in y divided by the difference in x. Electricity, a taxi and an hourly rate are typical examples. A fixed percentage per period is not linear, but exponential.

y=ax+by = ax + blinear model
a=y2−y1x2−x1a = \frac{y_2 - y_1}{x_2 - x_1}slope

Symbols

aaslopeNOK
bbstarting valueNOK
xxnumber of units

Example

Electricity: 49 NOK a month plus 1.20 NOK per kWh. At 500 kWh the price is 1.2⋅500+49=6491.2 \cdot 500 + 49 = 649 NOK.

The slope between (0, 49) and (500, 649) is 649−49500=1.2\dfrac{649 - 49}{500} = 1.2.

The slope is the change per unit.
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Part of Mathematics 1P: Linear models and graphs.