Full list of Formulae

Linear Equations and Functions

slope-intercept form: $y = m x + b$
where, $m$ is slope, $b$ is y-intercept form.
$s l o p e, m = \frac{c h a n g e s i n y}{c h a n g e s i n x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Linear Inequalities

Phrase	Translates to...
"More than $c$ ", "greater than $c$ ", or "higher than $c$ "	$> c$
"Less than $c$ " or "lower than $c$ "	$< c$
"Greater than or equal to $c$ " or "at least $c$ "	$\geq c$
"Less than or equal to $c$ " or "at most $c$ "	$\leq c$
"No less than $c$ "	$\geq c$
"No more than $c$ "	$\leq c$
"Least", "lowest", or "minimum" value	The smallest value that satisfies the inequality
"Greatest", "highest", or "maximum" value	The largest value that satisfies the inequality
"A possible" value	Any value that satisfies the inequality

Graph of Linear Inequalities

When a system of linear equations is graphed, the solution appears where the lines intersect.

When we have linear inequalities in slope-intercept form:

If $y$ is greater than $m x + b$ , shade above the line.
If $y$ is less than $m x + b$ , shade below the line.

In slope-intercept form, inequalities with...

Greater than ( $>$ ) or less than ( $<$ ) signs do not include points on the line in the solution set. We use a dashed line to show that the points on the line are not included.
Greater than or equal to ( $\geq$ ) or less than or equal to ( $\leq$ ) signs do include points on the line in the solution set. We use a solid line to show that points on the line are included.