Lines and their rules: cheat sheet

Linear relations · The words and methods from the lessons, with an example of each.

gradient

$m$ , the number in front of $x$ : one step right, the line goes up $m$ (down when $m$ is negative). A bigger $m$ is steeper; $m = 0$ is flat.

y = \mathbf{3}x + 1

vertical and horizontal lines

One letter: every point on $x = 3$ has $x = 3$ (a vertical line); every point on $y = -2$ has $y = -2$ (horizontal).

x = 3 \quad y = -2

y-intercept

$c$ , the number on its own: where the line crosses the $y$ -axis (at $x = 0$ ). Changing $c$ moves the line up or down without changing its steepness.

y = 2x + \mathbf{4}

parallel lines

The same $m$ gives the same steepness, so the lines never meet. $y = 2x + 4$ is $y = 2x + 1$ moved up 3.

y = 2x + 1 \quad y = 2x + 4

y = 2x + 1 and y = 2x + 4: same m, so parallel

inequality region

Draw the boundary $y = 2x + 1$ : dashed for $<$ and $>$ , solid for $\le$ and $\ge$ . Test a point such as $(0, 0)$ : true, shade its side; false, the other side.

y < 2x + 1

y < 2x + 1: below the dashed line, including (0, 0)