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Linear Equations Topics Review

Linear Equations Topics Review. Interactive Algebra. Welcome Back from Winter Break!. In the linear equations chapter we have learned about linear equations and graphs ( ________ _____ ). Today we will review the major concepts you have learned so far. straight lines. Use your notes….

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Linear Equations Topics Review

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  1. Linear Equations Topics Review Interactive Algebra

  2. Welcome Back from Winter Break! • In the linear equations chapter we have learned about linear equations and graphs ( ________ _____ ). • Today we will review the major concepts you have learned so far. straight lines

  3. Use your notes… Important concepts from Linear Equations & Functions section: • ______________________________________ • ______________________________________ • ______________________________________ STANDARD FORM: How to tell if an equation is linear: It’s a straight line, no exponents above 1, no variables in the denominator or square root, Determine if a point is on the graph of a linear equation by plugging in the point.

  4. Review Problems: • Write each equation in standard form: + 2x + 2x (4) (4) – x – x

  5. Use your notes… Important concepts from Using Intercepts: • ______________________________________ • ______________________________________ Use the cover-up method when an equation is in STANDARD FORM. The cover-up method works because the graph of a line will cross the y-axis when x = 0 AND it will cross the x-axis when y = 0.

  6. Review Problems (Intercepts): 3) Find the x- and y-intercepts: 4) x-int: 6; (6, 0) y-int: –2; (0, –2) Standard Form: – x – x x-int: 15; (15, 0) y-int: –3; (0, –3)

  7. Review Problems (Intercepts) Continued: • Use intercepts to graph the line given by each equation. 5) Standard Form: –6y –6y

  8. Use your notes… Important concepts from Slope: • _____________ • ______________________________________ Slope formula: To find the slope from a graph count the rise over the run. rise run m = _____________ ** Watch the slope formula song ** http://www.youtube.com/watch?v=g4Jg1N1YRGg

  9. Review Problems (Slope): • Find the slope of the line that contains each pair of points: (8, –16) and (4, –4) –16 (– 4) – 8 4 – m = m = m = _____________ _____________ _____________ –12 4 –3

  10. Review Problems (Slope): 7) Find the slope of the line that contains each pair of points: (1, –3) and (–1, –11) –3 (–11) – 1 (–1) – m = m = m = _____________ _____________ _____________ 8 2 4

  11. Review Problems (Slope) Continued: Find the slope of the line: (No need to write down) 7a) rise run run –6 rise 1 1 –6 m = m = m = _____________ ______ _____________ 1 – 6

  12. Review Problems (Slope) Continued: Find the slope of the line: (No need to write down) 7b) undefined NOT ZERO! m = _____________

  13. Review Problems (Slope) Continued: 7c) Find the slope of the line: 0 m = _____________

  14. Review Problems (Slope) Continued: Find the slope of each line. 7d) run 3 rise run rise 6 6 3 m = m = m = ______ _____________ _____________ 2

  15. Use your notes… Important concepts from Slope Intercept Form: • ___________________ • ______________________________________ • ______________________________________ Slope-intercept form: m = slope of the line; b = y-intercept To write y = mx + b given slope & a point (x, y), plug in the x & y and solve for b! ** Watch the slope-intercept song (55 secs)** http://www.youtube.com/watch?v=Yw4PdF-aMgA

  16. Review Problems (y=mx+b): 8) Slope = ½ and y-intercept = 9

  17. Review Problems (y=mx+b): • Write the equation of the line in slope-intercept form: 9) slope = 6, (3, –1) is on the line y m x Is (3, –1) the y-intercept? NO! Solve for the y-intercept (b). – 18 – 18

  18. Review Problems (y=mx+b): 10) Write the equation of the line in slope-intercept form & then graph the equation. Slope: & (6, –4) y x m rise: –1 run: 3 + 2 + 2

  19. Use your notes… Important concepts from Point-Slope Form: • _______________ • ______________________________________ • ______________________________________ Point-slope form: m = slope of the line; Given point: To change from point-slope to slope-intercept, distribute the mand get y by itself.

  20. Review Problem (Point-Slope Form): • Write an equation in slope-intercept form for the line given: 11) slope =3; (5, –1) 12) slope =–2; (–4, 17) –1 +17 –1 +17

  21. Review Problem (Point-Slope Form): • Write an equation in slope-intercept form for the line through two points: 13) (1, –2) and (3, 10) Step 1: _______________ Formula: Step 2: Substitute the slope and one of the points into the point-slope form: Find the slope. +10 +10

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