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2.2 Linear Equations

2.2 Linear Equations. SLOPE. SLOPE. RISE. RUN. Slope Formula. Given points (X 1 ,Y 1 ) and (X 2 ,Y 2 ). Is the same as ?. Example ( 4 , 0 ) and ( 7 , 6 ). (X 1 ,Y 1 ) (X 2 ,Y 2 ). Example ( -6 , 5 ) and ( 2 , 4 ).

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2.2 Linear Equations

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  1. 2.2 Linear Equations

  2. SLOPE SLOPE RISE RUN

  3. Slope Formula Given points (X1,Y1) and (X2,Y2) Is the same as ?

  4. Example( 4 , 0 ) and ( 7 , 6 ) (X1,Y1) (X2,Y2)

  5. Example( -6 , 5 ) and ( 2 , 4 ) (X1,Y1) (X2,Y2)

  6. Example( 5 , 2 ) and ( -3 , 2 ) (X1,Y1) (X2,Y2)

  7. Example( 2 , 7 ) and ( 2 , -3 ) (X1,Y1) (X2,Y2)

  8. Recap of slope

  9. Linear Forms of Linear EquationsStandard Form (AX + BY = C) FINDING INTERCEPTS • A and B cannot be fractions. • A cannot be negative To find y-intercept, set x = 0 Y-intercept (0,-5) To find x-intercept, set y = 0 X-intercept (5/3,0) y = 3x – 5 y – 3x = – 5 – 3x + y = – 5 3x – y = 5

  10. Linear Forms of Linear EquationsSlope Intercept Form (y = mx + b) FINDING INTERCEPTS • Y is isolated on one side. • Y is positive To find y-intercept, set x = 0 Y-intercept (0,-3) To find x-intercept, set y = 0 X-intercept (6,0) x – 2y = 6 –2y = – x + 6 y = ½ x + 6/-2 y = ½ x – 3

  11. Find a line|| to 2x + 4y = -8and passes thru (8,3) Slope intercept • Use y = mx + b • y = - 1/2x + b • Plug in point • 3 = - ½ (8) + b • 3 = -4 + b • 7 = b FINAL EQUATION y = mx + b y = - ½ x + 7 First find slope 2x + 4y = -8 4y = -2x – 8 y = - ½ x – 2 Slope

  12. Find a linePerpendicular to 3x – 2y = 10and passes thru (-6,2) Slope intercept • Use y = mx + b • y = -2/3 x + b • Plug in point • 2 = -2/3 (-6) + b • 2 = 4+ b • -2 = b FINAL EQUATION y = mx + b y = -2/3x - 2 c First find slope 3x – 2y = 10 - 2y = -3x + 10 y = 3/2 x – 5 Slope

  13. Find a lineThat has slope = 2and passes thru (-4,7) Slope intercept • Use y = mx + b • y = 2x + b • Plug in point • 7 = 2(-4) + b • 7 = -8 + b • 15 = b FINAL EQUATION y = mx + b y = 2 x + 15

  14. Find a lineThat has x-intercept = (5,0)and y-intercept (0,-3) Slope intercept • Use y = mx + b • y = 3/5 x + b • Plug in point either one ! • 0 = 3/5 (5) + b • 0 = 3 + b • -3 = b FINAL EQUATION y = mx + b y = 3/5 x - 3 • First find slope • m • m = 3/5

  15. First Let’s Review . . . Graphing Linear Equations

  16. Graph x = 3

  17. Graph y = -3

  18. Graph Y = -3/4 x + 2 Y = mx + b m = slope b = y-intercept • Plot the y-intercept first • Starting from the y-intercept, go up if + or down if – Then go right. 3) Plot point and draw your line. m = -3 / 4 b = 2

  19. Graph 5x + 6y < 30 5x + 6y < 30 6y< -5x + 30 Y < -5/6 x +5

  20. Graph 2x + 4y ≥ 16 2x + 4y ≥ 16 4y ≥ -2x + 16 Y ≥ -2/4 x + 4 Y ≥ -1/2 x + 4

  21. Graph 5x - y < 8 5x – y < 8 – y < -5x + 8 y > 5x – 8

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