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2.4.2 – Parallel, Perpendicular Lines

2.4.2 – Parallel, Perpendicular Lines. We know how to quickly graph certain linear equations Y = mx + b Slope-intercept Y-intercept as a starting point; slope to find a second point Ax + by = c Standard Form Use the x and y intercepts as the two points.

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2.4.2 – Parallel, Perpendicular Lines

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  1. 2.4.2 – Parallel, Perpendicular Lines

  2. We know how to quickly graph certain linear equations • Y = mx + b • Slope-intercept • Y-intercept as a starting point; slope to find a second point • Ax + by = c • Standard Form • Use the x and y intercepts as the two points

  3. Now, we will compare two lines/equations and their graphs • Two lines may be: • 1) Parallel • 2) Perpendicular • 3) Neither

  4. Parallel Lines • Given two lines, they are considered parallel if and only if they have the same slope; m1 = m2 • The lines never intersect; run off in the same direction • “Air” between them

  5. Example. Tell whether the following lines are parallel or not. • 1) y = 3x + 4, y – 3x = 10 • 2) -4x + y = -6, y = 4x • 3) y – x = 1, y = -x

  6. Example. Graph the equation y = 3x + 4. Then, graph a line that is parallel and passes through the point (1, 1).

  7. Example. Graph the equation y = -x + 5. Then, graph a line that is parallel and passes through the point (1, 1).

  8. Perpendicular Lines • Two lines are perpendicular, if and only if, their slopes are negative reciprocals OR their product is -1 • OR m1(m2) = -1 • Graphically, two perpendicular lines intersect at a 90 degree angle

  9. Example. Tell whether the following lines are perpendicular, parallel, or neither. • 1) y = 3x + 4, y = (-1/3)x – 5 • 2) y = 4x – 5, y = 10 + 4x • 3) y = (x/2) – 9, y + (2/x) = -6 • 4) y = x – 1, y = -x

  10. Example. Graph the equation y = 3x + 4. Then, graph a line that is perpendicular and passes through the point (1, 1).

  11. Example. Graph the equation y = -x + 5. Then, graph a line that is perpendicular and passes through the point (1, 1).

  12. Horizontal and Vertical Lines • Horizontal Lines = lines of the form y = a; must have a “y-intercept” • Vertical Lines = lines of the form x = a; must have a “x-intercept” • General Rule; must be able to see the line, so cannot draw a line on top of the axis

  13. Example. Graph the equation x = 3.

  14. Example. Graph the equation y = -4.

  15. Assignment • Pg. 91 • 33-49 odd, 50-53, 60, 62, 69, 70

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