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Linear Functions By: Elizabeth A. and Valarie P.

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Definition: A function is a linear function if F(X)=ax+b, for real numbers A and B. When a linear function is written in the form Ax+By=C, it is said to be in standard form. The graph of a linear function is a straight line. To graph a linear function, find at least two of its ordered pairs, plot them, and draw a line through them.

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Examples: Graph 5x-2y=10 Solution

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Examples (cont.) Let x= 0.5(0)-2y= 10 -2y= 10 Y= -5 (0,-5) Let x= 0will give us the y-intercept Solve for y

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Let y= 0.5x-2(0)= 10 5x= 10 X= 2 (2,0) Let y= 0 will give us the x-intercept

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Examples (cont.) Let x= 4.5(4)-2y= 10 20-2y= 10 -2y= -10 Y= 5 (4,5) 3 rd point is a check These points would be plotted and a line drawn through them to complete the graph.

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Pictures

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This is a picture of the Chapel Bridge in Lucern, Switzerland. The roof of this footbridge, originally constructed in 1333, can be modeled by a linear function. The origin is set at the base of the stone tower. Given this somewhat arbitrary origin, the roof of the bridge could be modeled by the function y = 0.25x + 2.

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Review Definition: A linear function is a polynomial of degree one. The graph of a linear function is a straight line. The rate of change of a linear function is called the slope of the function. In a linear function, the average and instantaneous rate of change are always the same. Formula for a Linear Function: General Form: Slope-Intercept Form: Point-Slope Form: Two-Point Form:

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Review (cont.) You need only two points to graph a linear function. These points may be chosen as the x and y intercepts of the graph for example. Determine the x intercept, set f(x) = 0 and solve for x. 2x + 4 = 0 x = -2 Determine the y intercept, set x = 0 to find f(0). f(0) = 4 The graph of the above function is a line passing through the points (-2, 0) and (0, 4) as shown below.

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