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Aim: What is the relationship between slopes of parallel lines?

Aim: What is the relationship between slopes of parallel lines?. Do Now: a. y = 2 x + 5 b. y = 2 x – 1 c. y = 2 x + 2. 2. What is the slope of each line?. 2. 2. Slopes of Parallel Lines. Graph Equations a), b), and d) on the graphing calculator by

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Aim: What is the relationship between slopes of parallel lines?

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

  2. Slopes of Parallel Lines • Graph Equations a), b), and d) on the graphing calculator by • 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 havingequalslopes are parallel. Lines havingdifferent slopes are not parallel.

  3. Model Problem • Points A(-4, 2), B (1, 2), C(1, -3) and D(-4, -3) form a quadrilateral. • Graph the points and draw quadrilateral ABCD • What are the slopes of sides AB, BC, CD and AD? • What kind of quadrilateral is ABCD? Explain

  4. y 9 8 7 6 5 4 3 2 1 (-4, 2)A B(1, 2) -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 -1 -2 5 units -3 -4 -5 (-4, -3)D C(1, -3) -6 5 units -7 -8 -9 Model Problem 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 Slope of AB = 0 Slope of AD = undefined Slope of CD = 0 Slope of BC = undefined 4 equal sides 4 right angles SQUARE

  5. 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. Just showing the graph is not enough - prove using the formula for slope. C (3,4) D (3,2) (0,1) B (0,-1) A 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.

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

  7. (0, 1) (4, 3) (2, 2) (0, -4) Model Problem Graph a line that is parallel to the line y = 1/2x – 4 and that passes through point (2, 2) y = mx + b m = 1/2 b = -4 y = 1/2x – 4 What is the equation of this new line? y = 1/2x + 1 m = 1/2 b = 1

  8. Model Problem 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 2nd time for Equation. On your calculator, sent the new equation Y1=

  9. Model Problem Graph a line that is parallel to the line y = 2x + 1 and that passes through (0, -2).

  10. Model Problem Graph a line that is parallel to the line y = -4x – 5 and that passes through (0, 2).

  11. Model Problem Graph a line that is parallel to the line y = -4 and that passes through (0, -6).

  12. Model Problem Graph a line that is parallel to the line y = 1/3x – 6 and that passes through (1, 2).

  13. Model Problem Graph a line that is parallel to the line 2y = 4x – 6 and that passes through (-2, -4).

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