1. Parallel and Perpendicular Lines Chap 4 Supplemental Lecture

2. Forms of Lines Recall: EquationDescription x = k Vertical Line, x-intercept k, undefined slope y = k Horizontal Line, y-intercept k, slope is 0 y = mx + b Slope-intercept form, slope m, y- intercept b y - y 1 = m(x - x 1 ) Point-slope form, slope m, the line passes through (x 1, y 1 ) Ax + By = C General form

3. Review: Writing an Equation Given the Slope and the y-intercept Example: Write the equation of the line with a slope of –2/3 and a y-intercept of 6.

4. Review: Writing an Equation Given a Point and a Slope Example: Write the equation of the line that passes through (-4, 3) with a slope of 5/4.

5. Parallel and Perpendicular Lines Parallel lines- They have the same slopes. Perpendicular lines- lines that never intersect. lines that intersect at right angles. (90  angles.) They have negative reciprocal slopes.

6. Parallel Lines on the Calculator Graph y = – 2x + 5 and y = –2x + 1 on your calculator. What do you notice?

7. Perpendicular Lines on the Calculator Graph y = 3/4x + 3 and y = –4/3x + 1 on your calculator. Since your calculator screen is wider than it is tall, the standard viewing window is stretched and perpendicular lines will not look . Hit ZOOM and choose 5:square to square the viewing window.

8. Relating Lines Example: Determine if the lines are parallel, perpendicular, or neither. Show your work and explain your answer. a)4x – 3y = 6 and 3x + 4y = 8

9. Relating Lines Example: Determine if the lines are parallel, perpendicular, or neither. Show your work and explain your answer. b) 3x + 2y = 8 and 6y = 5 – 9x

10. Relating Lines Example: Determine if the lines are parallel, perpendicular, or neither. Show your work and explain your answer. c) 4x = 2y + 3 and 2y = 2x + 3

11. Writing Lines Example: Write the equation of a line that goes through: a) the point (3, 4) and is parallel to 4x – 2y = 5.

12. Writing Lines Example: Write the equation of a line that goes through: b) the point (6, 8) and is perpendicular to y = 2x – 3.

13. Writing Lines Example: Write the equation of a line that goes through: c) the point (-3, 2) and is perpendicular to y = 5.