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Key Concepts, continued To find the x-intercept in function notation, set f(x) = 0 and solve for x. The x-intercept has the coordinates (x, 0). To locate the x-intercept of a graphed function, determine the coordinates of the line where the line crosses the x-axis : Graphing Linear Functions
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IntroductionIn this lesson, different methods will be used to graph lines and analyze the features of the graph. In a linear function, the graph is a straight line with a constant slope. All linear functions have a y-intercept. The y-intercept is where the graph crosses the y-axis. If a linear equation has a slope other than 0, then the function also has an x-intercept. The x-intercept is where the function crosses the x-axis.
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3.4.1: Graphing Linear Functions
Key Concepts• To find the y-intercept in function notation, evaluate
f(0).
• The y-intercept has the coordinates (0, f(0)).
• To locate the y-intercept of a graphed function, determine the coordinates of the function where the line crosses the y-axis.
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3.4.1: Graphing Linear Functions
Key Concepts, continued• To find the x-intercept in function notation, set f(x) = 0
and solve for x.
• The x-intercept has the coordinates (x, 0).
• To locate the x-intercept of a graphed function, determine the coordinates of the line where the line crosses the x-axis.
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3.4.1: Graphing Linear Functions
Key Concepts, continued• To find the slope of a linear function, pick two
coordinates on the line and substitute the points into
the equation , where m is the slope, y2 is the
y-coordinate of the second point, y1 is the y-coordinate
of the first point, x2 is the x-coordinate of the second
point, and x1 is the x-coordinate of the first point.
• If the line is in slope-intercept form, the slope is the x
coefficient. 4
3.4.1: Graphing Linear Functions
Key Concepts, continuedGraphing Equations Using a TI-83/84:
Step 1: Press [Y=].
Step 2: Key in the equation using [X, T, q, n] for x.
Step 3: Press [WINDOW] to change the viewing window, if necessary.
Step 4: Enter in appropriate values for Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl, using the arrow keys to navigate.
Step 5: Press [GRAPH].
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3.4.1: Graphing Linear Functions
Key Concepts, continuedGraphing Equations Using a TI-Nspire:
Step 1: Press the home key.
Step 2: Arrow over to the graphing icon (the picture of the parabola or the U-shaped curve) and press [enter].
Step 3: Enter in the equation and press [enter].
Step 4: To change the viewing window: press [menu], arrow down to number 4: Window/Zoom, and click the center button of the navigation pad.
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3.4.1: Graphing Linear Functions
Key Concepts, continuedStep 5: Choose 1: Window settings by pressing the center
button.
Step 6: Enter in the appropriate XMin, XMax, YMin, and YMax fields.
Step 7: Leave the XScale and YScale set to auto.
Step 8: Use [tab] to navigate among the fields.
Step 9: Press [tab] to “OK” when done and press [enter].
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3.4.1: Graphing Linear Functions
Common Errors/Misconceptions• incorrectly plotting points
• mistaking the y-intercept for the x-intercept and vice versa
• being unable to identify key features of a linear model
• confusing the value of a function for its corresponding x-coordinate
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3.4.1: Graphing Linear Functions
Guided PracticeExample 2Given the function , use the slope and
y-intercept to identify the x-intercept of the function.
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3.4.1: Graphing Linear Functions
Guided Practice: Example 2, continued1. Identify the slope and y-intercept.
The function is written in f(x) = mx + b
form, where m is the slope and b is the y-intercept.
The slope of the function is .
The y-intercept is 2.
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3.4.1: Graphing Linear Functions
Guided Practice: Example 2, continued2. Graph the function on a coordinate plane.
Use the y-intercept, (0, 2), and slope to graph the function. Be sure to extend the line to cross both the x- and y-axes.
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3.4.1: Graphing Linear Functions
Guided Practice: Example 2, continued3. Identify the x-intercept.
The x-intercept is where the line crosses the x-axis. The x-intercept is (10, 0).
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3.4.1: Graphing Linear Functions
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3.4.1: Graphing Linear Functions
Guided Practice: Example 2, continued
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Guided PracticeExample 3Given the function , solve for the x- and
y-intercepts. Use the intercepts to graph the function.
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3.4.1: Graphing Linear Functions
Guided Practice: Example 3, continued1. Find the x-intercept.
Substitute 0 for f(x) in the equation and solve for x.
Original function
Substitute 0 for f(x).
Subtract 4 from both sides.
x = 3 Divide both sides by .
The x-intercept is (3, 0).
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3.4.1: Graphing Linear Functions
Guided Practice: Example 3, continued2. Find the y-intercept.
Substitute 0 for x in the equation and solve for f(x).
Original function
Substitute 0 for x.
Simplify as needed.
f(x) = 4
The y-intercept is (0, 4).16
3.4.1: Graphing Linear Functions
Guided Practice: Example 3, continued3. Graph the function.
Plot the x- and y-intercepts.
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3.4.1: Graphing Linear Functions
Guided Practice: Example 3, continuedDraw a line connecting the two points.
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3.4.1: Graphing Linear Functions
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3.4.1: Graphing Linear Functions
Guided Practice: Example 3, continued
