4.1 Linear functions  (Page 14/27)

Key concepts

• Linear functions can be represented in words, function notation, tabular form, and graphical form. See [link] .
• An increasing linear function results in a graph that slants upward from left to right and has a positive slope. A decreasing linear function results in a graph that slants downward from left to right and has a negative slope. A constant linear function results in a graph that is a horizontal line. See [link] .
• Slope is a rate of change. The slope of a linear function can be calculated by dividing the difference between y -values by the difference in corresponding x -values of any two points on the line. See [link] and [link] .
• An equation for a linear function can be written from a graph. See [link] .
• The equation for a linear function can be written if the slope $m$ and initial value $b$ are known. See [link] and [link] .
• A linear function can be used to solve real-world problems given information in different forms. See [link] , [link] , and [link] .
• Linear functions can 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 equation for a linear function can be written by interpreting the graph. See [link] .
• The x -intercept is the point at which the graph of a linear function crosses the x -axis. See [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] .

Section exercises

Verbal