Graph of Linear Function of One Variable

Theorem

Let $f: \R \to \R$ be a linear function of one variable expressed by the equation:

$\map f x = a_0 + a_1 x$

The graph of $f$ in a cartesian plane consists of a straight line:

whose $y$-intercept is $a_0$

whose slope is $a_1$.

Proof

Expressing $f$ in the form $y = \map f x$, we have:

$y = a_0 + a_1 x$

Thus it is in the same form as the slope-intercept form of an equation of a straight line in the plane.

Hence the result.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): linear function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): linear function