2.4 Linear Functions: Graphs and Slopes

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2.4 Linear Functions Graphs and Slopes
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• Slope is the steepness of the line (the slant of
  the line) and is defined by
• rise the change in y
• run the change in x
• y2 y1 y1 y2
• x2 x1 x1 x2

m

or
SLOPE IS ALSO CALLED AS THE RATE OF CHANGE
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Find the slope of the line that goes through
these 2 points

1. (1,5) (2,7)
2. (2,3) (1,3)

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• Slope intercept form
• y mx b
• m is the slope, b is the y-intercept

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• Y intercept shows whether the graph shifted up
  or down
• Example
• Y 2x slope is 2, y-intercept is ___
• Y 2x 5 slope is 2, y-intercept is ___
• Y 2x 3 slope is 2, y-intercept is ___

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• Find the slopes and the y-intercepts
• y ½ x 4
• Slope is ½ and y-intercept is 4
• 5x 4y 8
• -4y -5x 8
• y 5/4 x - 2
• Slope is 5/4 and y-intercept is -2

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• Find the linear equation if you know slope m 3
  and y-intercept is (0,4)
• We have y mx b
• So y 3x 4

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Graphing using slopes and y-intercepts

• Start by plotting y-intercept (0,b)
• From there, use the slope rise / run
• If , go up, or right
• If - , go down or left

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Y 3x 2 Step 1 Start with the y-intercept
(0,2)
Step 2 Slope is 3/1 so we rise 3 (up 3) and run
1 (to the right 1)
Step 3 Connect 2 points, we will have the
function y 3x - 2
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More problems

1. Y (1/2)x 3
2. Y (-3/4)x 1
3. Y -2x - 2

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More examplesWriting functions

1. Open a new business with the initial cost is
   100,000. Profit is 500 per day. Write the
   profit function for d number of days.
2. Bought a new car for 40,000. The value of the
   car depreciates at a rate of 100 per day. Write
   the value function for d number of days.