# Linear Equations

## Slope of a Line

The slope is the slant of a line.  All diagonal lines have a slope. Horizontal lines have a slope of 0. Vertical lines have an undefined slope.

Lines that slant upward, towards Quadrant I in the coordinate plane (where x and y are both positive), have positive slopes.

## Solving for Variables Using Graphs/Coordinates

Remember, every linear equation forms a line.  Each line contains a set of points whose coordinates are given as $(x, y)$.  The coordinates $(x,y)$ not only show the points on the line, but they provide the $x$ and $y$ variables in the linear equations (e.g., in $y = mx + b$).

If you are given a coordinate (or both coordinates) of a point on a line, you can plug those coordinates into the x and y of the linear equation.

## Standard Form of a Line

There are many ways to write a linear equation (an equation that represents a line).  When we graph a line, we like to put it in $y=mx+b$ form, because that makes it easy to find the slope and the y-intercept.  But, lines can also be given in standard form.

Standard form is:

$Ax+By=C$

Essentially the $x$ term comes first, added to the $y$ term, equal to the number (which we call $C$).

## Slope Intercept Form of a Line

Every linear equation can be represented by a line (thus, the name linear equation!).  The equations take the form of $y=mx+b$.  (There are other ways to write linear equations, but $y=mx+b$ is the easiest form for graphing and finding the graphs of a line.

$y=mx+b$ has several components: