2. Aim: Slopes of Parallel Lines Course: Applied Geometry Do Now: a. y = 2x + 5 b. y = 2x – 1 c. y = 2x + 2 Aim: What is the relationship between slopes of parallel lines? What is the slope of each line? 2 2 2

3. Aim: Slopes of Parallel Lines Course: Applied Geometry Slopes of Parallel Lines Graph Equations a), b), and d) on the graphing calculator by 1.Clicking the Y = button and inputting Y1 = 2x + 5 Y2 = 2x – 1 Y3 = 2x + 2 2. Click the Graph key and watch the graphs appear. Hit the Trace key and skip from line to line. Lines having equal slopes are parallel. Lines having different slopes are not parallel.

4. Aim: Slopes of Parallel Lines Course: Applied Geometry Points A(-4, 2), B (1, 2), C(1, -3) and D(-4, -3) form a quadrilateral. a.Graph the points and draw quadrilateral ABCD b.What are the slopes of sides AB, BC, CD and AD? c.What kind of quadrilateral is ABCD? Explain Model Problem

5. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem y 123456789 -2-3-4-5-6 1 2 3 4 5 6 7 8 9 -2 -3 -4 -5 -6 -7 -8 -9 B(1, 2) (-4, 2)A C(1, -3) (-4, -3)D 5 units 4 equal sides 4 right angles SQUARE Slope of AB = 0 Slope of CD = 0 Slope of AD = undefined Slope of BC = undefined Recall: Two lines are parallel if their slopes are equal and if the slopes of two lines are equal, the lines are parallel. AB || CD & AD || BC

6. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Quadrilateral ABCD has vertices A(0,-1), B(0,1), C(3,4), and D(3,2). Using coordinate geometry, determine what type of quadrilateral ABCD is. A B C(3,4) (0,1) (0,-1) (3,2)D Just showing the graph is not enough - prove using the formula for slope. Since the slope of BC and AD are the same, the lines are parallel. Since the slope of AB and CD are the same, the lines are parallel. BC || AD, AB || CD, ABCD is a parallelogram.

7. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = 2x – 2 and that has a y-intercept of 4 What is the equation of this new line? (0, 4) (1, 6) (0, -2) y = 2x - 2 y = 2x + 4 m = 2 b = 4 y = mx + b b = -2

8. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = 1/2x – 4 and that passes through point (2, 2) What is the equation of this new line? m = 1/2 y = 1/2x – 4 y = 1/2x + 1 y = mx + b m = 1/2b = 1 (4, 3) (2, 2) (0, -4) b = -4 (0, 1)

9. Aim: Slopes of Parallel Lines Course: Applied Geometry On Sketchpad: Graph a line that is parallel to the line y = -1/4x + 3 and that passes through (3, 0). Sketchpad: Graph  Plot New Function  y = -1/4x + 3  Enter Graph  Plot Points  (3, 0)  Plot Plot a second point that would result in a line parallel to y = -1/4x + 3 Highlight new line  Measure  Slope and a 2 nd time for Equation. On your calculator, sent the new equation Y 1 = Model Problem

10. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = 2x + 1 and that passes through (0, -2).

11. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = -4x – 5 and that passes through (0, 2).

12. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = -4 and that passes through (0, -6).

13. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = 1/3x – 6 and that passes through (1, 2).

14. Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line 2y = 4x – 6 and that passes through (-2, -4).