1 / 21

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 ).

yelena
Télécharger la présentation

2.2 Linear Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related