Graphing and Finding Slope of Lines - Concept 17, 18, 19, 20

1. Concept 17: Slope

2. right 2 Up 4

4. Finding Slope • A(2, 5) B(-3, 7) • C(-3, 0) D(5, -4) • E(2, -3) F(-3, -3) • G(2, 6) H(-3, -4)

5. Graphing Slope of Lines • Step 1: • Plot the given ordered pair. • Step 2: • Determine what the slope means and graph the slope from the given ordered pair. (repeat from new ordered pair) • Step 3: • Determine the opposite slope and graph it from the given ordered pair. (repeat from new ordered pair) • Step 4: • Draw a line through all points with a straight edge.

6. Graphing slope of Lines • m= , (-2, 3) 2. m= -3, (4, -1)

7. Graphing slope of Lines • 3. m= 0, (-2, -4) • 4. m= undefined, (3, 5)

8. Graphing and Writing Equations Using Slope-Intercept Form Concept 18

9. Steps for graphing a line using Slope-Intercept form • Step 1: • Rewrite equation in slope-intercept form • y = mx + b • Step 2: • Identify the slope (m) and y-intercept (b) • Step 3: • Plot the y-intercept (b) • Step 4: • Use the slope (m) to plot additional points (starting from the y-intercept) • Example: x + 2y = 4 • 2y = -x + 4 2 Slope: m = y-intercept: b = 2

10. Graph each equation. 1. y = 8 2. y = x + 3 3. y = –2x Slope: m = Slope: m = Slope: m = y-intercept: b = 8 y-intercept: b = 0 y-intercept: b = 3

11. 4. y = x – 1 5. y = 3x – 5 6. x = -3 Slope: m = Slope: m = Slope: m = y-intercept: b = -1 y-intercept: b = -5 y-intercept: b = none x-intercept: -3

12. Writing Equations of Lines • Slope intercept form: • y = mx + b slope Y-intercept • a slope of 3 and a • y-intercept of -2. • y = (3)x + (-2) • y = 3x – 2 a slope of −1 4 and a y-intercept of 5. y = ( y = x + 5

13. Write the equation of each line with the given information. Equation of line s b = 2 y = -2x + 2 Equation of line r b = 3 y = 1x + 3 • Equation of line t • b = -3 • 3 • y = 3x + (-3) Equation of line u b = -5 y = x + (-5)

14. Point-Slope form: slope Ordered pair • 7. Passes through (6, 3) and has a slope of 2. • 8. Passes through (8, -4) and has a slope of .

15. 9. Passes through (0, 4) and (6, 13) • 10. Passes through (6, -4) and (9, -9)

16. Undefined slope.

17. Slopes of parallel and Perpendicular Lines Concept 19

18. Slope of parallel lines In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. Any two horizontal lines are parallel. Line a Line b parallel

19. Line a Line b Not parallel

20. Slope of Perpendicular Lines In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is -1. Horizontal lines are perpendicular to vertical lines. Line a Line b Not perpendicular

21. Line a Line b perpendicular

22. Determine if the ordered pairs for are parallel, perpendicular or neither. A(-1, 5) B(3, -2), 6. A(-3, 5), B(0, 1),   X(5, 6), Y(1, 13) X(2, -7), Y(-2, -10) parallel perpendicular

23. Determine if the ordered pairs for are parallel, perpendicular or neither. 7. A(-2, 1) B(3, -9), 8. A(1, 15), B(8, 1), X(1,0), Y(3, -1) X(-5, 6), Y(2, -8) parallel neither

24. Steps for graphing parallel and perpendicular lines. 1) Find the slope of a line that is given. 2) Determine what slope to use for new line (same or opposite reciprocal). 3) Graph other ordered pair and use the correct slope. New line New line

25. Graph the line that satisfies each condition. 1. Passes through (1, 1), parallel to line l containing points (2, 4) and (5, 1). 2. Passes through (−1, 5), perpendicular to line l containing points (0, −2) and (6, 6). New line New line

26. 3. Passes through (1, -2), parallel to line l containing points (-2, 1) and (1, 5). 4. Passes through (4, 4), perpendicular to line l containing points (-4, 3) and (0, -3). New line New line

27. Finding distance between points and lines Concept 20

28. Line m contains points (-5, 3) and (4, -6). Find the distance between the line and point P(2, 4) Step 1: ___________ the line given and find its ____________. Step 2: Graph the point given and the _________________ _______________ of the slope in step 1 until it crosses the line. Reciprocal slope = m = Step 3: Determine the _________ _____ where the lines _____________. What is the ordered pair? Step 4: Find the ________________ between the points. Graph slope opposite reciprocal ordered pair intersect (-2, 0) distance

29. Find the distance between line l and point P.1. Line l contains (0, 0) and (-5, 5). Point P is at (1,5) New line (1, 5) and (-2, 2)

30. 2. Line l contains (5, -1) and (-4, 2). Point P is at (4, 6) (4, 6) and (2, 0) New line

31. 3. Line l is y = 2x + 2 and point P is at (-6, 0) (-6, 0) and (-2, -2) New line

32. 4. Line l is y = x – 4 and point P is at (-2, 6) (-2, 6) and (4, 2) New line

33. Distance between two parallel lines 1) Graph each line on the coordinate plane. 2) Find the slope of a line perpendicular to the lines and graph it from one of the lines y-intercepts until it crosses the other line. • Draw a segment that connects the two lines. • Using the endpoints of the segment, find the distance. (0, 4) and (3, -5) Perpendicular segment

34. 2. y = -2 y = 5 Distance: 5+2 = 7

35. 3. Perpendicular segment (0, 9) and (-4, 8)