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Understanding Secant Lines in Linear Functions

Explore the concept of secant lines cutting through a curve, understanding their slopes with the given function y = 2x + 6, and how they depict constant slope characteristics in linear functions.

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Understanding Secant Lines in Linear Functions

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  1. UNIT 1B LESSON 3 SLOPE OF A SECANT

  2. P2 P3 P1 P2 P1 DEFINITION: A secantis a line that cuts a curve in two or more distinct points.

  3. D(0, 6) C(-1, 4) B(-2, 2) A(-3, 0) For the function y = 2x + 6 draw the curve (graph). Draw the secant lines through the points AB and CD. Slope of CD Slope of AB 4 0 6 2 • 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.

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

  5. Finish the Question on page 2

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