Graphing Linear Functions

Every straight-line graph can be written as

where $m$ is the gradient (steepness and direction) and $c$ is the $y$-intercept (where the line crosses the $y$-axis, i.e. the value of $y$ when $x = 0$).

Reading a line's equation. For $y = 2x + 1$: the gradient is $2$ and the line crosses the $y$-axis at $(0, 1)$.

Intercepts are the anchor points for sketching:

• $y$-intercept: set $x = 0$.
• $x$-intercept: set $y = 0$ and solve for $x$.

Worked example. For $y = 2x - 6$, the $y$-intercept is $-6$. For the $x$-intercept, set $y = 0$: $0 = 2x - 6$, so $2x = 6$ and $x = 3$. The line passes through $(0, -6)$ and $(3, 0)$.