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Chapter 4 – Coordinate Geometry: The Straight Line

Chapter 4 – Coordinate Geometry: The Straight Line. James Kim Michael Chang Math 10 Block : D. Table of Contents. 4.1 – Using an Equation to Draw Graph 4.2 – The Slope of a Line 4.3 – The Equation of a Line :Part 1 4.4 – The Equation of a Line :Part 2

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Chapter 4 – Coordinate Geometry: The Straight Line

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  1. Chapter 4 – Coordinate Geometry:The Straight Line James Kim Michael Chang Math 10 Block : D

  2. Table of Contents 4.1 – Using an Equation to Draw Graph 4.2 – The Slope of a Line 4.3 – The Equation of a Line :Part 1 4.4 – The Equation of a Line :Part 2 4.5 – Interpreting the Equation (Ax+By+C=0)

  3. 4.1 - Using an Equation to Draw a Graph Equation of a Line Property • The coordinates of every point on the line satisfy the equation of the line • Every point whose coordinates satisfy the equation of the line is on the line

  4. 4.1 - Using an Equationto Draw a Graph • A basic equation y=mx+b m equals slope b equals y-intercept

  5. 4.1 - Using an Equation to Draw a Graph Example (Using a calculator) Equation/ Y=2X+3 1. On a TI-83 Graphic calculator, go to Y= and type 2X+3 forY1 2. Press window, and type numbers. (X min=-10, X max=10, X sc1=1, Y min=-10, Y max=10, Y sc1=1 X res=1) 3. Press graph You would get this on your graph -

  6. 4.1 - Using an Equationto Draw a Graph Example (No calculator) Equation/ Y=2X+3 1. You solve for Y, when X equals 1, 2, 3. You would get 5, 7, 9 for Y. 2. You draw zooms on the grid - - - 3. You draw line through the zooms - -

  7. 4.2 - The Slope of a Line Constant Slope Property • The Constant Slope Property allows us to define the slope of a line to be the slope of any segment of the line • The Constant Slope Property is used to draw a line passing through a given point with a given slope • If the slope of two lines are equal, the lines are parallel • Conversely, if two non-vertical lines are parallel. Their slopes are equal. • If the slopes of two lines are negative reciprocals, the lines are perpendicular • Conversely, if two lines are perpendicular, their slopes are negative reciprocals

  8. 4.2 - The Slope of a Line Example For this graph, the coordinates are given, which are (1,-1) and (-2,3) So the slope of this line segment is M = (3-(-1)) / (-2-1) The slope for this line is 4/-3

  9. 4.3- The Equation of a Line:Part 1 • The graph of the equation y = mx+b is a straight line with slope m and y-intercept b • Draw a graph with equation y=mx+b.

  10. 4.3 – The Equation of a Line Part 1 • Example Equation y=4x-3 The slope is 4 and y intercept is –3 In calculator, go to Y=, and put Y1= 4x-3 - - Then, press graph button and you will get - -

  11. 4.4 - The Equation of a Line:Part 1 • Ax + By + C = 0 • Standard form of the equation of a line • Collinear – Coordinates in the same straight line

  12. 4.4 - The Equation of a Line:Part 1 4 Cases of solving the Equation of a line Case 1 : Given two coordinates Case 2 : Given slope and y-intercept Case 3 : One coordinate and the slope Case 4 : Slope and the x-intercept

  13. Case #1 – Given two coordinates • Example (4,3) , (7,9) Find the slope 1. M = (9-3) / (7-4) = (6/3) = 2 2. Y = 2x + b 3. Choose 1 point to substitute 4. Y = 2x=b 3 = 2(4) + b b = -5 5. Y = 2x-5

  14. Case #2 – Given slope and y -intercept • Example 1. m = -2, y-int = or b=6 2. y = mx+b 3. y = -2x +6

  15. Case #3 – Given one coordinate and the slope • Example (x,y) = (3,-1) , m=2 1. Y = 2x+b 2. –1= 6+b 3. –7=b 4. Y = 2x-7

  16. Case #4 – Givenslope and the x -intercept • Example m = 5 , x-int = 3 (3,0) 1. Y = 5x+b 2. 0 = 5(3)+b 3. –15 = b 4. Y= 5x-15

  17. 4.5- Interpreting the Equation Ax + By + C = 0 • Determining the slope, x- intercept, and y-intercept Ax + By + C = 0 By = -Ax –C Y = -(-A/B) + (-C/B) • Slope = (-A/B) • Y intercept = (-C/B) • Ax = -C • X = (-C/A) • X intercept = (-C/A)

  18. 4.5- Interpreting the Equation Ax + By + C = 0 • Example Find slope, y-int, and x-int for this equation. Graph the equation 2x + 4y + 8 = 0 1. Slope : (-A/B) = (-2/4) = (-1/2) 2. Y-int : (-C/B) = (-8/4) = (-2) 3. X-int : (-C/A) = (-8/2) = (-4) 4. Equation : y = (-1/2)x -2 5. Graph : - - - - - - - - - - - - - - - -

  19. The END

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