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Geometry Warm-Up: Linear Equations and Graphs

Solve linear equations, convert to standard form, graph equations, and find intercepts. Learn about slope-intercept and point-slope forms. Homework questions included.

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Geometry Warm-Up: Linear Equations and Graphs

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  1. Day 10 Geometry

  2. Warm Up 1) Solve for y 3x – 2y = 6 2) Put the following into slope-intercept form and graph y – 5 = 4 (x + 2)

  3. Homework Check • Show answers to Slope Worksheet / Graphs

  4. Learning Objective • G-GPE-5 - Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

  5. Note #12 Point-Slope Form of a Linear Equation y – y1 = m(x – x1) Given slope (m) and a point (x1 , y1) Ex. Write the equation of the line through the point (–1,4) with slope of 3 in both point-slope form and slope intercept form.

  6. Note #12 (continued) • Ex. Write an equation in point-slope and slope-intercept form of the line with slope –8 that contains the point (3,–6).

  7. Note #12 (continued) • Write the equation of a line through the points (–2,3) and (1,–1). First find the slope. Then use one of the two points and write the equation using point-slope form and slope- intercept form.

  8. Note #12 (continued) You Try: Write an equation in point-slope form and slope-intercept form of the line that contains the points (4,–9) and (–1,1).

  9. Note 13 Standard Form of a linear equation Ax + By = C A, B, and C cannot be fractions A is always a positive number

  10. Note #13 (continued) Convert y = –2x + 5 to standard form Convert y = (3/5)x – 7 to standard form

  11. Note #13 (continued) Graphing from Standard Form using Intercepts x–intercept = y–intercept =

  12. Note #13 (continued) Find the x and y intercepts of the equation 3x + 4y = 12

  13. Note #13 (continued) Find the intercepts of the equation and then graph the line 2x + 3y = 6

  14. Note #13 (continued) Find the intercepts of the equation 1/3x + 5/6y = –3/2

  15. Exit Slip 1) Write an equation in point-slope form that goes through the points (1, –4) and (3,2). 2) Graph the equation 3x – 2y = 12 using the intercept method Homework: P. 155 #11 – 22 All

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