parallel and perpendicular lines chap 4 supplemental lecture
TRANSCRIPT
Parallel and Perpendicular LinesChap 4 Supplemental Lecture
Forms of LinesRecall:
Equation Description
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 - y1 = m(x - x1) Point-slope form, slope m, the line passes through (x1, y1)
Ax + By = C General form
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.
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.
Parallel and Perpendicular LinesParallel 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.
1 2m m
21
1m
m
Parallel Lines on the CalculatorGraph y = – 2x + 5 and y = –2x + 1 on your calculator. What do you notice?
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.
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
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
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
Writing Lines
Example: Write the equation of a line that goes through:
a) the point (3, 4) and is parallel to 4x – 2y = 5.
Writing Lines
Example: Write the equation of a line that goes through:
b) the point (6, 8) and is perpendicular to y = 2x – 3.
Writing Lines
Example: Write the equation of a line that goes through:
c) the point (-3, 2) and is perpendicular to y = 5.