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- Linear functions
- Linear functions
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
and initial value
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,
See
[link] .
- Vertical lines are written in the form,
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,
and using the
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
Terry is skiing down a steep hill. Terry's elevation,
in feet after
seconds is given by
Write a complete sentence describing Terry’s starting elevation and how it is changing over time.
Terry starts at an elevation of 3000 feet and descends 70 feet per second.
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Jessica is walking home from a friend’s house. After 2 minutes she is 1.4 miles from home. Twelve minutes after leaving, she is 0.9 miles from home. What is her rate in miles per hour?
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A boat is 100 miles away from the marina, sailing directly toward it at 10 miles per hour. Write an equation for the distance of the boat from the marina after
t hours.
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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