Equations of Lines

• Point-Slope Form: If a line has slope $m$ and passes through the point $(x_1 , y_1,)$ then an equation of the line is $y-y_1=m(x-x_1).$
• Slope-Intercept Form: If a line has slope $m$ and y-intercept $(0 , b),$ then an equation of the line is $y=mx+b.$
• Standard Form: Any line has an equation of the form $Ax+By=C,$ where $A,B,C$ are real and $A$ and $B$ are not both 0. $A,B,C$ should share no common factors, e.g. $x+2y=4$ is preferable to $2x+4y=8.$ Additionally, some prefer $A$ to be nonnegative.
• Vertical Line: An equation of the vertical line passing through $(a , b)$ is $x=a.$ Vertical lines have undefined slope.
• Horizontal Line: An equation of the horizontal line passing through $(a , b)$ is $y=b.$ Horizontal lines have slope 0.
• Parallel Lines: Two distinct nonvertical lines are parallel if and only if they have the same slope.
• Perpendicular Lines: Two lines, neither of which are vertical, are perpendicular if and only if their slopes have a product of -1, i.e. if a line has slope $m$ , then a perpendicular line has slope $-1/m.$