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1.2 Linear Equations in Two Variables

1.2 Linear Equations in Two Variables. Writing linear equations. How do we define Slope. Rise over Run. The change of y over the change in x Given point (x 1 , y 1 ) and (x 2 , y 2 ). Find Slope through two points. Lets the points by (6, 10) and (5, -3) So the slope would be

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1.2 Linear Equations in Two Variables

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  1. 1.2 Linear Equations in Two Variables Writing linear equations

  2. How do we define Slope

  3. Rise over Run • The change of y over the change in x • Given point (x1, y1) and (x2, y2)

  4. Find Slope through two points • Lets the points by (6, 10) and (5, -3) • So the slope would be • So the slope is or just 13

  5. Slope-intercept formy = mx + b m is for slope; b is the y intercept We do we use m for Slope and b for the intercept? What is the slope of

  6. Horizontal lines and Vertical lines • Horizontal line have zero slopes. • Vertical line have undefined slopes. Why?

  7. m = When (y1) – (y2) = 0, there is no rise in the line. The fraction would equal zero When (x1) – (x2) = 0, it makes the fraction undefined. The dominator of a fraction can near be zero.

  8. What is the difference of a ratio and a rate or rate of change • Ratio have the same units • Rate have different units

  9. Writing Linear Equations in 2 variables • Point-Slope form • Lets write equation using the points (580,50) and (625,47) • The slope would be

  10. Using one of the two points • Using the point (580, 50)

  11. The General form a line • Ax + By + C = 0 • A, B and C are not all zero or fractions • Multiply both sides by 15 to get rid of fractions, then add x and subtract 580.

  12. Parallel and Perpendicular Lines • Parallel lines have the same slope • Perpendicular line have negative reciprocal slopes

  13. Test for Parallel or Perpendicular • Given 2 lines with sets of points Line1: (0,8) and (4, 5) Line 2: (6, 10) and (0, 2) Find the slopes of each line

  14. Line 1: has slope Line 2: have slope So what are the lines?

  15. Homework • Pages 21-24 # 2,8,12,16,22,26,30,34,38,40,46,48,52,56, 60,64,68,72,76,80,84,88

  16. Homework • Page 21 – 26 # 13, 25, 41, 51, 79, 89, 101, 107, 117, 123, 134

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