Transcript Lesson 3.6

*
*
*If two nonvertical lines are parallel,
their slopes are equal
*If the slopes of two distinct non
vertical lines are equal, they are
parallel
*Any two vertical lines are parallel
*
*𝑚 =
𝑦2 −𝑦1
𝑥2 −𝑥1
where (𝑥1 , 𝑥2 ) 𝑎𝑛𝑑 (𝑦1 , 𝑦2 )
*Example: Find the slope of the line with
points (1,3) and (-4, -5)
*
8
5
*
* If lines are parallel they should have the same slope.
(1, 5)
(3, 3)
n
m
(-2, -4)
(1, -4)
*
*If line n contains (-4, 2) and (3, 1) and line m
contains (-4, 0) and (8, -2) are the lines parallel?
*
*Slope intercept form is 𝑦 = 𝑚𝑥 + 𝑏 where m =
slope and b = y-intercept.
*Write in slope intercept form
*1. 3𝑥 + 4𝑦 = 12
*2. −2𝑦 − 6𝑥 = 10
*
*Are the lines 4𝑦 − 12𝑥 = 20 𝑎𝑛𝑑 𝑦 = 3𝑥 − 1
parallel?
*
*Are the lines parallel?
1
*𝑦 = − 2 𝑥 + 5 𝑎𝑛𝑑 2𝑥 + 4𝑦 = 9
*
*Point slope form 𝑦 − 𝑦1 = 𝑚(𝑥 −
*
*Write an equation for the line parallel to 𝑦 = −4𝑥 + 3
that contains (1, -2).
*Step 1: identify the slope of the given line 𝑦 = −4𝑥 + 3
*Step 2: use point slope form to write an equation for the
new line.
*
*Write an equation for the line parallel to 𝑦 = −𝑥 + 4 that
contains (-2, 5).
*Step 1: identify the slope of the given line 𝑦 = −𝑥 + 4
*Step 2: use point slope form to write an equation for the
new line.
*
*If two non vertical lines are perpendicular, the product
of their slopes is -1.
*If the slopes of two lines have a product of -1, the lines
are perpendicular (Opposite reciprocals)
*Any horizontal line and vertical line are perpendicular
*
*
*Line n contains (0, 5) and (3, -2) and line m
contains (5, 5) and (-4, 1). Are they
perpendicular?
*
*Write an equation for the line perpendicular to y =
− 3𝑥 − 5 that contains (-3, 7).
*Step 1: identify the slope of the line y = −3𝑥 − 5
*Step 2: find the slope of the perpendicular line. The
slopes should be opposite reciprocals
*Step 3. use point slope form to write the new equation
*
*Find the equation for the line perpendicular to
5𝑦 − 𝑥 = 10 that contains (15, -4)
*
* Pg. 161-162 # 1-23, 25-30