Graphs of linear equations and functions

A linear graph is a straight line, and $y = mx + b$ tells you everything about it: $m$ is the slope and $b$ the $y$-intercept.

The slope is rise over run — how far the line climbs for each step right A positive slope rises left to right, a negative slope falls, and a slope of zero gives a horizontal line. A vertical line has no defined slope at all, because the run is zero.

The y-intercept is where the line crosses the $y$-axis, which is the value of $y$ when $x = 0$. The $x$-intercept is the mirror image: set $y = 0$ and solve.

Two facts about pairs of lines are tested constantly. Parallel lines have equal slopes. Perpendicular lines have slopes whose product is $-1$, so a line perpendicular to one with slope $\frac{3}{2}$ has slope $-\frac{2}{3}$.

Many questions never ask you to draw anything. They give two points and ask for the equation, or give an equation and ask what the slope means in context — in which case the slope is always a rate, something per something.

Find the slope of the line through $(2, 4)$ and $(6, 16)$.
Apply the formula directly

A line has slope $\frac{3}{2}$ and passes through $(0, 1)$. Write its equation.
The point $(0, 1)$ is the $y$-intercept, so $b = 1$ and