Linear equations 2-2 a graphing and x-y intercepts

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Transcript of Linear equations 2-2 a graphing and x-y intercepts

  • 1. Graphs & Linear Equations Y X y=mx+b

2. A Point Y X (X,Y)is called anOrdered Pair The X value or X Coordinate is the location of a point in the X direction The Y value or Y Coordinate is the location of a point in the Y direction (X,Y)(4,3) 3. How to Graph a Point Y X (X,Y) (4,2) X is the distance along the x=axis Y is the distance along the y=axis 1234 321 HINT: Think of the x-axis as the Number Line -4-3-2-1 0 X 1234 -4-3-2-1 0 HINT: Think of the y-axis a vertical Number Line Y 3210-1 -2 4. Important Vocabulary for Graphs Y X x-axis y-axis The Graph itself is called the x-y plane (ie. Plane surface) or The Coordinate Plane or Cartesian Coordinate Plane after Renee Descartes 1st Quadrant 2nd Quadrant 3rd Quadrant 4th Quadrant Quadrants start with Positive X & Y and go Counter Clockwise (+X,+Y) (+X,-Y) (-X,-Y) (-X,+Y) 5. Graphing Linear Equations (Find 3 Domain & Range Points) First Degree Equations are Lines (y=mx+b) and you calculate 3 (X,Y) values Make sure the points line up on a x-y graph and connect the dots. 6. RECALL X-Domain & Y-Range y = 2x-7when theDomain is {-2, 0, 2} f(-2) = 2(-2) -7 = -4 -7 = -11(-2,-11) f(0) = 2(0) -7 = 0 -7 = -7(0,-7) f(2) = 2(2) -7 = 4 -7 = -3(2,-3) Answer: RANGE: {-11, -7, -3} Graphing Lines is just like finding the Range of 3 Domain Points: (Substitute each Domain value into the equation) 7. Practice Finding 3 Points Given a Linear Equation Find any 3 (X,Y) points for the following equations: y=5x y=4x-5 y=3x+1 (Hint: Try x=0) 8. Sample Solutions

  • xy= 5x
  • 00
  • 5
  • 10

xy= 4x-5 xy= 3x+1 9. Now Graph the 3 Points

  • xy= 5x
  • 00
  • 5
  • 10

(0,0) (1,5) (2,10) 10. What is Intercept in Math? Y X An Intercept is the coordinate where a line crosses the x or y axis 11. Using X&Y Intercepts to Graph a Line The X intercept is the x coordinate (where a line crosses the x axis). Y X x-axis y-axis (0, 2 ) ( 3 ,0) The Y intercept is the y coordinate (where a line crosses the y axis). 12. Name the X&Y Intercepts Y X x-axis y-axis (0, 2 ) ( 3 ,0) 13. Name the X&Y Intercepts Y X x-axis y-axis (0, 2 ) ( -2 ,0) 14. Name the X&Y Intercepts Y X x-axis y-axis 15. Name the X&Y Intercepts Y X x-axis y-axis 16. What is the value of x at the y intercept?What is the value of Y at the x-intercept? Y X x-axis y-axis 17. Find the x- and y-intercepts. 1.x - 2y = 12 x-intercept:Plug in0for y. x - 2( 0 ) = 12 x = 12;(12, 0) y-intercept:Plug in0for x. 0- 2y = 12 y = -6;(0, -6) 18. Find the x- and y-intercepts. 2.-3x + 5y = 9 x-intercept:Plug in0for y. -3x - 5( 0 ) = 9 -3x = 9 x = -3;(-3, 0) y-intercept:Plug in0for x. -3( 0 ) + 5y = 9 5y = 9 y =;(0,) 19. What is the x-intercept of 3x 4y = 24?

  • (3, 0)
  • (8, 0)
  • (0, -4)
  • (0, -6)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 20. What is the y-intercept of -x + 2y = 8?

  • (-1, 0)
  • (-8, 0)
  • (0, 2)
  • (0, 4)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 21. Graph y = 2x - 6using x&y intercepts 1st Make x-y table XY= 2x - 6 Y X x-axis y-axis Graph Linear Eq. 22. Graph y = 2x - 6using x&y intercepts 1st Make x-y table 2nd Set x = 0 and solve for y XY= 2x - 6 0-6 Y X x-axis y-axis (0,-6) Graph Linear Eq. 23. Graph y = 2x - 6using x&y intercepts 1st Make x-y table 2nd Set x = 0 and solve for y 3rd Set y = 0 and solve for x

  • XY= 2x - 6
  • 0-6
  • 0

Y X x-axis y-axis (0,-6) (3,0) Graph Linear Eq. 24. Graph y = 2x - 6using x&y intercepts 1st Make x-y table 2nd Set x = 0 and solve for y 3rd Set y = 0 and solve for x 4thPlot these 2 points anddraw line

  • XY= 2x - 6
  • 0-6
  • 0

Y X x-axis y-axis (0,-6) (3,0) Graph Linear Eq. 25. Graph y = 2x - 6using x&y intercepts 1st Make x-y table 2nd Set x = 0 and solve for y 3rd Set y = 0 and solve for x 4thPlot these 2 points anddraw line 5th Use 3rd point to check

  • XY= 2x - 6
  • 0-6
  • 0
  • 42

Y X x-axis y-axis (0,-6) (3,0) (4,2) Graph Linear Eq. 26. Graphing Horizontal & Vertical Lines Y X x-axis y-axis This line has a y value of 4 for any x-value.Its equation isy = 4 (meaning y always equals 4) 27. Graphing Horizontal & Vertical Lines Y X x-axis y-axis This line has a x value of 1 for any y-value.Its equation isx = 1 (meaning x always equals 1) 28. The Equation of a Vertical Line isX=ConstantY X x-axis y-axis x = 1 29. The Equation of a Horizontal Line isY=ConstantY X x-axis y-axis y = 3 30. Graph the following lines Y = -4 Y = 2 X = 5 X = -5 X = 0 Y = 0 31. Answers Y X x-axis y-axis x = 5 x = -5 32. Answers Y X x-axis y-axis y = -4 y = 2 33. Answers Y X x-axis y-axis x = 0 y = 0