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1 UNIT 1B LESSON 3 SLOPE OF A SECANT

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DEFINITION: A secant is a line that cuts a curve in two or more distinct points. P1P1 P2P2 P1P1 P2P2 P3P3 2

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For the function y = 2x + 6 draw the curve (graph). Draw the secant lines through the points AB and CD. XY=2x+6 A-3 B-2 0 2 XY=2x+6 C D0 4 6 Slope of ABSlope of CD 3 The slope of the secant on a linear function, through any two points will be the slope of the line. In this case the slope is 2. This shows that a line is the only curve of constant slope. B(-2, 2) A(-3, 0) C(-1, 4) D(0, 6)

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For the function draw the curve and the secant lines through the points AC, BD, and BE. XY A B0 C1 D2 E3 -3 1 -2 1 A(-1,1) B(0,-2) C(1, -3) D(2, -2) E(3, 1) Equation of AC Equation of BD Equation of BE y = x – 2 Notice: The slopes of secants on curves change as the points change. Slopes may be positive, zero or negative. 4 EXAMPLE U1B L3 Page 1 m = 0

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Finish the Question on page 2 5

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