3.5: Lines in the Coordinate Plane Objective: To graph and write equations of lines.
Introduction In this lesson, different methods will be used to graph lines and analyze the features...
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Transcript of Introduction In this lesson, different methods will be used to graph lines and analyze the features...
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