DescriptionThe graph of a linear equation is a line. Linear equations can be written in several different forms, including slope-intercept form, , point-slope form, , and standard form, . Vertical lines have the form , and horizontal lines have the form . 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 - or -axis are called the intercepts. To find the -intercept, let . To find the -intercept, let .
- The steepness of a line can be described by the slope. The slope of a line is the ratio of the change in -values to the change in -values of any two points on the line.
- The equation of a nonvertical line with slope and -intercept can be written in the slope-intercept form .
- The equation of a nonvertical line with slope that passes through the point can be written in the point-slope form .
- The standard form of a line is . It is typically used for determining the - and -intercepts of a line.
- Equations of vertical and horizontal lines are based on an undefined or zero slope. Vertical lines have the form , and horizontal lines have the form , where and are real numbers.
- Parallel lines have the same slope but different -intercepts.
- Perpendicular lines have slopes whose product is –1.