The equation of a line consists of a multiple of $x$ plus some constant: \[ f(x) = mx+b. \]

• $m$ is the slope.
• $b$ is the $y$-intercept. The value of the function when $x=0$.
• $b/m$ is the $x$-intercept. Another word for $x$-intercept is root, i.e., a value where $f(x)=0$.

• There is a unique linear function that passes through any two points $(x_1,y_1)$ and $(x_2,y_2)$ if $x_1 \neq x_2$.
• The inverse function of $f(x)=\frac{1}{m}(x-b)$.

Here is the graph of \[ f(x) = 2x - 3. \]

A line can also be described in a more symmetric form. \[ Ax + By = C, \] This is known as the general equation of a line. We have $b=\frac{C}{B}$ and $m=\frac{-A}{B}$.