# Graphing Lines

## Overview

### Description

The graph of a linear equation is a line. Linear equations can be written in several different forms, including slope-intercept form, $y = mx + b$, point-slope form, $y-y_1=m(x-x_1)$, and standard form, $Ax + By = C$. Vertical lines have the form $x = a$, and horizontal lines have the form $y = b$. Parallel lines have the same slope, and perpendicular lines have slopes with a product of –1. Lines can be graphed by plotting points or by using key features identified in their equations. The equation of a line can be written from a graph by using the coordinates of points located on the graph.

### At A Glance

• A linear equation can be graphed by using a table to generate a list of ordered pairs. When all the ordered pairs are plotted, they lie on the same line.
• The points where a line crosses the $x$- or $y$-axis are called the intercepts. To find the $x$-intercept, let $y = 0$. To find the $y$-intercept, let $x = 0$.
• The steepness of a line can be described by the slope. The slope of a line is the ratio of the change in $y$-values to the change in $x$-values of any two points on the line.
• The equation of a nonvertical line with slope $m$ and $y$-intercept $b$ can be written in the slope-intercept form $y = mx + b$.
• The equation of a nonvertical line with slope $m$ that passes through the point $(x_1, y_1)$ can be written in the point-slope form $y-y_1=m(x-x_1)$.
• The standard form of a line is $Ax + By = C$. It is typically used for determining the $x$- and $y$-intercepts of a line.
• Equations of vertical and horizontal lines are based on an undefined or zero slope. Vertical lines have the form $x = a$, and horizontal lines have the form $y = b$, where $a$ and $b$ are real numbers.
• Parallel lines have the same slope but different $y$-intercepts.
• Perpendicular lines have slopes whose product is –1.