# Linear Equations A linear equation represents a line. **The standard form of a linear equation is $y=kx+n$ where $k$ is the line's *slope* and $n$ is the *$y$-intercept*.** **The slope of a linear equation is known as "rise over run" as it shows the change of $y$ (rise) for a change of $x$ (run).** $k=\frac{\Delta y}{\Delta x}$ **The slope can also be thought of as the $\tan$ of the angle the line forms with the $x$-axis.** ## Non-standard forms ### The Point-Slope Form The point-slope form can be used to construct a line from a point ($a,b$) and the line's slope. $y=k(x-a)+b$ ### The Two-Intercepts Form The two-intercepts form can be used to construct a line from the two intercepts. Given $x$-intercept ($\frac{c}{a},0$) and $y$-intercept ($0,\frac{c}{b}$) $\frac{a}{c}x + \frac{b}{c} y = 1$