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Equations of Lines in the Coordinate Plane

Equations of Lines in the Coordinate Plane. Section 3.7 p.189. Graphing Linear Equations. Definitions : Cartesian Coordinate Plane – a graph X – axis – the horizontal axis of a coordinate plane Y – axis – the vertical axis of a coordinate plane. Graphing Linear Equations.

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Equations of Lines in the Coordinate Plane

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  1. Equations of Lines in the Coordinate Plane Section 3.7 p.189

  2. Graphing Linear Equations • Definitions: • Cartesian Coordinate Plane – a graph • X – axis – • the horizontal axis of a coordinate plane • Y – axis – • the vertical axis of a coordinate plane

  3. Graphing Linear Equations • Definitions: • Origin – where the two axes meet (0,0) • Ordered pair – • x and y values of a point on a graph • Also called a point of a set of coordinates • Quadrants – the four sections that the x and y axes divide the coordinate plane into – named I, II, III, and IV

  4. Coordinate Plane • Identify • Origin • Y-axis • X-axis • Quadrants I, II, III, and IV

  5. “Rise Up Run Out” • Slope • “Steepness” • What are some examples where slope is a factor? grade of a road, incline of wheelchair ramp, pitch of a roof, etc.

  6. Slope of a Line • Slope • = • = • Pick any two points on a line to compute the slope

  7. Determine the slope of a line given the coordinates of two points on the line • Given A (-1,2) and B (4, -2) • Find the slope of line AB

  8. Find the slope of the segment below • (5, 4) and (3, -1) • Slope = • m= =

  9. Positive vs. negative slope • Positive slope- rises to the right • Negative slope- falls to the right

  10. Slope • Horizontal line • Slope = ∆y = 0 = 0 ∆x ∆x • Vertical line • Slope = ∆y = ∆y = undefined ∆x 0

  11. Given C (4, 0) and D (4, -2) • Find the slope of line CD • undefined

  12. Slope of a Line • Special cases: • x = 4 • What will this slope be? • y = - 3 • What will this slope be?

  13. Slope-Intercept Form • Given • What is the slope? • What are the coordinates of the y-intercept? • (0, -5)

  14. Graph y = x -5

  15. Point-Slope Form • = ) • Given point A (3, 5) on the line with a slope of -1, find the equation of the line in point-slope form. • = ) • Write the equation of this line in slope-intercept form. • =

  16. What is the equation of a line in point-slope form passing through point A(-2,-1) and B(3, 5)? • First find the slope; • Then plug one of the points into the point-slope form of the line;

  17. More Practice • What is the equation of a line in slope intercept form with slope of -2 and a y-intercept of (0, 5)? • In point-slope form? • y- 5 = -2(x-0) • What is the equation in point-slope form of the line through (-1, 5) with a slope of 2? • In slope-intercept form?

  18. Homework • P.194-195 #9-41 odd • Additional Practice • 13-2 Slope of a Line worksheet

  19. How do you think the slopes of parallel lines compare? • What about perpendicular lines?

  20. Slopes of Parallel Lines (GSP)

  21. Slopes of Perpendicular Lines (GSP)

  22. 3.8 Slopes of Parallel and Perpendicular Lines • Two non-vertical lines are parallel if and only if their slopes are equal. • (parallel lines have the same slope) • Two non-vertical lines are perpendicular if and only if the product of their slopes is -1 • (slopes of perpendicular lines are negative reciprocals of each other) • m1 *m2 = -1 or m1= -1/m2

  23. Are the two lines below parallel? • y= -3x +4 and y=-3x -10 • y= 4x-10 and y=2x-10 • y= x +5 and y = x +7 • Are the two lines below perpendicular? • y= 4x – 2 and y= -x +5 • y= -x +4 and y= x +4 • y=x -10 and y= +5

  24. Given a line through points (5,-1) and (-3, 3), find the slope of all lines • A. parallel to this one • B. perpendicular to this one • Slope = (-1 – 3)/ (5 – (-3)) = -4/8 = -1/2 • A. slope = -1/2 • B. slope = 2

  25. Are the two lines below perpendicular? • (-4, 2) and (0, -4) • (-5, -3) and (4, 3)

  26. Homework • p.201-203 #7-10, 15-18, 23, 25, 31, 33 • 13-3 Parallel and Perpendicular Lines worksheet • 13-7 Writing Linear Equations worksheet #11-23 odd, 24-26 all

  27. Find the distance between points A and B A B Two points in a horizontal line Distance = absolute value of the difference in the x-coordinates Distance=|-2 – 2| = 4 or |2 – (-2)| = 4

  28. Find the distance between points A and B A B Two points in a vertical line Distance = absolute value of the difference in the y-coordinates Distance=|-8 – 3| = 11 or |3 – (-8)| = 11

  29. What about two points that do not lie on a horizontal or vertical line? • How can you find the distance between the points? • The distance between two points is equal to the length of the segment with those points as the endpoints

  30. The Distance Formula • The distance between points (x1, y1) and (x2, y2) is given by: • d = • Find the distance between (0, 0) and (7, 24) • d = • d = 25

  31. Midpoint Formula Review • Find the midpoint of the line segment with endpoints (4, 7) and (-2, 5) • (1, 6)

  32. Class work • 13-1 Distance Formula worksheet • 13-5 Midpoint Formula worksheet

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