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Notes 5-3B

Learn how to convert linear equations to slope-intercept form, graph real-world equations, and master plotting with examples and practice problems in this comprehensive guide.

kennethparker
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Notes 5-3B

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  1. Notes 5-3B Objective: Convert linear equations to slope intercept form and graph real-world equations.

  2. Ax + By = C x- intercept (let y = 0) 3x + 2(0) = 12 3x = 12 x = 4 y-intercept (let x = 0) 3(0) + 2y = 12 2y = 12 y = 6 REVIEW: Standard Form: Graph 3x + 2y = 12 using x and y intercepts.

  3. New way to do this problem….. Put the equation into slope-intercept form (solve for y) 3x + 2y = 12 -3x -3x 2y = -3x + 12 2 2 2 y = -3 x + 6 2

  4. Graph it! y = -3 x + 6 2 y- intercept is 6 slope is -3 Plot a point at (0,6). Then go down 3 and to the right 2. Plot another point. Continue this pattern. 2

  5. Put each equation into slope-intercept form and graph the equation: 2x – 5y = 10 2x – y = -6 y = 2/5x - 2 y = 2x + 6

  6. EXAMPLE: The Smith’s plant a maple tree that is 5 feet tall. The tree grows an average of 1 ½ feet per year. Write and graph an equation that models this situation. Starting height: 5 (y-int) Change: 1 ½ or 1.5 (slope) Equation: y = 1.5x + 5

  7. Equation: y = 1.5x + 5 x y 8 7 6 5 4 3 2 1 0 1 2 5 6.5 8 0 1 2 3 4 5 6

  8. EXAMPLE: A farmer is planting crops. He has 28 acres already planted and is planting 6 more each day. Write and graph an equation that models this situation. Starting amt: 28 (y-int) Change: 6 (slope) Equation: y = 6x + 28

  9. Equation: y = 6x + 28 x y 44 42 40 38 36 34 32 30 28 26 0 1 2 28 34 40 0 1 2 3 4

  10. YOUR TURN: Convert each to slope intercept form: • – 5x + y = 10 • 4x + 2y = 8 • y – 5 = 4(x – 2) y = 5x + 10 y = -2x + 4 y = 4x – 3

  11. Homework: Lesson 5-3, page 276 #34, 36, 38, 40-46, 51-55 Quiz 5-1 to 5-3 Wednesday!

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