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Linear functions

A linear function has a straight line as its graph. The slope $a$ tells how much $y$ increases when $x$ increases by 1, and the constant term $b$ is where the graph crosses the $y$ -axis. If you know two points on the line, you can find both $a$ and $b$ .

Try it yourself

The linear function

f(x) = ax + b

linear function

a = \frac{y_2 - y_1}{x_2 - x_1}

slope through two points

Symbols

$a$	slope
$b$	constant term

Example

The line through $(1, 3)$ and $(4, 9)$ : $a = \frac{9 - 3}{4 - 1} = 2$ and $b = 3 - 2\cdot 1 = 1$ , so $f(x) = 2x + 1$ .

Check by inserting the other point:

f(4) = 9

Practise functions for free →

← The square identities · Quadratic functions →

Part of Mathematics 1T: Functions.