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+by = mx + b, point-slope form, yy1=m(xx1)y-y_1=m(x-x_1), and standard form, Ax+By=CAx + By = C. Vertical lines have the form x=ax = a, and horizontal lines have the form y=by = 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 xx- or yy-axis are called the intercepts. To find the xx-intercept, let y=0y = 0. To find the yy-intercept, let x=0x = 0.
  • The steepness of a line can be described by the slope. The slope of a line is the ratio of the change in yy-values to the change in xx-values of any two points on the line.
  • The equation of a nonvertical line with slope mm and yy-intercept bb can be written in the slope-intercept form y=mx+by = mx + b.
  • The equation of a nonvertical line with slope mm that passes through the point (x1,y1)(x_1, y_1) can be written in the point-slope form yy1=m(xx1)y-y_1=m(x-x_1).
  • The standard form of a line is Ax+By=CAx + By = C. It is typically used for determining the xx- and yy-intercepts of a line.
  • Equations of vertical and horizontal lines are based on an undefined or zero slope. Vertical lines have the form x=ax = a, and horizontal lines have the form y=by = b, where aa and bb are real numbers.
  • Parallel lines have the same slope but different yy-intercepts.
  • Perpendicular lines have slopes whose product is –1.