2.2 Graphs of linear functions  (Page 9/15)

Key concepts

• Linear functions may be graphed by plotting points or by using the y -intercept and slope. See [link] and [link] .
• Graphs of linear functions may be transformed by using shifts up, down, left, or right, as well as through stretches, compressions, and reflections. See [link] .
• The y -intercept and slope of a line may be used to write the equation of a line.
• The x -intercept is the point at which the graph of a linear function crosses the x -axis. See [link] and [link] .
• Horizontal lines are written in the form, $f(x)=b.$ See [link] .
• Vertical lines are written in the form, $x=b.$ See [link] .
• Parallel lines have the same slope.
• Perpendicular lines have negative reciprocal slopes, assuming neither is vertical. See [link] .
• A line parallel to another line, passing through a given point, may be found by substituting the slope value of the line and the x - and y -values of the given point into the equation, $f(x)=mx+b,$ and using the $b$ that results. Similarly, the point-slope form of an equation can also be used. See [link] .
• A line perpendicular to another line, passing through a given point, may be found in the same manner, with the exception of using the negative reciprocal slope. See [link] and [link] .
• A system of linear equations may be solved setting the two equations equal to one another and solving for $x.$ The y -value may be found by evaluating either one of the original equations using this x -value.
• A system of linear equations may also be solved by finding the point of intersection on a graph. See [link] and [link] .

Section exercises

Verbal

Algebraic

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: