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Graphing Linear Equations

Graphing Linear Equations. TEKS. 3 Different Forms. Point-Slope Form. Two Points Given. Slope-Intercept Form. 3 Forms. Two Points Known. (-1, -1) and ( 1,3) Plot both points Connect points. y. x. Calculate Slope. Two Points Known: Slope. (-1, -1) and ( 1,3) Calculate Slope:. y.

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Graphing Linear Equations

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  1. Graphing Linear Equations TEKS

  2. 3 Different Forms Point-Slope Form Two Points Given Slope-Intercept Form

  3. 3 Forms Two Points Known • (-1, -1) and ( 1,3) • Plot both points • Connect points y x Calculate Slope

  4. Two Points Known: Slope • (-1, -1) and ( 1,3) • Calculate Slope: y x Point-Slope Form

  5. 3 Forms Point-Slope Form • Point: (1,3) • Plot point • Slope: 2 (or ) • Rise 2, Run 1 • Plot point (2,5) • Connect points y x Place in equation

  6. Point-Slope Form Point (1,3);Slope 2 (,; slope: Plug into equation: y x Slope-Intercept Form

  7. 3 Forms Slope-Intercept Form • y = mx + b • y = 2x + 1 • y-intercept: 1 • Plot point (0,1) • Slope 2 (or ) • Rise 2, run 1 • Plot point (1,3) y x Changes in Slope Changes in Intercept

  8. Slope-Intercept Changes in Slope Intercept is held constant at y = 1 Negative Slope (m < 0) Positive Slope (m > 0) Slope m = 0

  9. Slopes Positive Slope • y = 2x + 1 • Slope = +2 • Rise 2, run 1 • Line is: • up to right • down to left y x

  10. Slopes Slope = 0 • No x-value • y = 0x + 1; y = 1 • Slope = 0 • y-intercept = 1 Line is horizontal y x

  11. Slopes Negative Slope • y = -2x + 1 • Slope = -2 • Rise -2, run 1 • Line is: • up to left • down to right y x

  12. Slope-Intercept Changes in Intercept Slope is held constant at 2 Negative Intercept (b < 0) Positive Intercept ( b > 0) Intercept b = 0 No Intercept

  13. Intercepts Positive Intercept • y = 2x + 1 • Intercept = +1 • Line intersects y-axis: • Above x-axis • Point (0,1) y x

  14. Intercepts Intercept = 0 • y = 2x + 0;y = 2x • Intercept = 0 • Line intersects y-axis: • At x-axis • Point (0,0) y x

  15. Intercepts Negative Intercept • y = 2x - 1 • Intercept = -1 • Line intersects y-axis: • Below x-axis • Point (0,-1) y x

  16. Intercepts No Intercept • No y-value • 0 = 2x – 4 • 2x = 4; x = 2 • Line intersects x-axis at (2,0) • Line does not intersect y-axis Line is vertical y x

  17. START TEKS Reference §111.32. Algebra I (One Credit). (b)  Knowledge and skills. (6)  Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to: (C)  investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b; (D)  graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y‑intercept;

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