Transcript Parallel and Perpendicular Lines - mathemons

Parallel and Perpendicular
Lines
Write the equation of a line that passes
through a given point, parallel to a given line.
Write the equation of a line that passes
through a given point, perpendicular to a
given line.
Parallel lines
Lines in the same plane
that do not intersect
are called parallel
lines. Parallel lines
have the same slope.
Perpendicular Lines
Lines that intersect at
right angles are called
perpendicular lines.
The slopes of these
lines are opposite
reciprocals.
Opposite reciprocals????
3…..
1
 ...
4
From the given equations, determine if the corresponding lines are
parallel, perpendicular, or neither.
y = 2x + 2
y = 4x - 2
neither
2x + 6y = 1
4x + 12y =3
parallel
1
y  x2
5
y  5 x  1
perpendicular
Write the slope intercept form of an equation for the line
that passes through (12,3), and is parallel to the graph of
y = 4x – 5
Using the same slope we have m = 4 and
(12,3)
Point-slope form
y – 3 = 4 ( x – 12 )
y – 3 = 4x – 48
y = 4x – 48 + 3
y = 4x - 45
Write the slope intercept form of an equation for the line
that passes through (3,5), and is perpendicular to the graph
of
y=½x–5
Using the negative reciprocal of the slope
we have, m = -2
Point-slope form
y – 5 = -2 ( x – 3 )
y – 5 = -2x + 6
y = -2x + 6 + 5
y = -2x + 11
Write an equation
that is parallel to
y= 3x – 8 and
passes through
the point ( 2, 5 )
Write an equation
that is parallel to
y= -2x – 8 and
passes through
the point ( 1, -2 )
Write an equation
that is parallel to
y= 7x + 1 and
passes through
the point ( -4, -2 )
Write an equation
that is perpendicular
to y= -8x + 1 and
passes through the
point ( 1, 6 )
Write an equation
that is perpendicular
to y= 2/3x + 6 and
passes through the
point ( 1, 7 )
Bell Work
1. Find the equation of
a line that passes
through the point (1, 6)
and perpendicular to
y = - ½ x – 5.
2. Find the equation of
a line that passes
through the point (-2, 4)
and perpendicular to
y = - ¼ x – 5.
3. Find the equation of
a line that passes
through the point (-3, 1)
and perpendicular to
y = - 1/8 x – 5.
4. Find the equation of
a line that passes
through the point ( 6,-2)
and perpendicular to
y = 2/3 x – 11.
5. Find the equation of
a line that passes
through the point ( 2, 9)
and perpendicular to
y = -3/4 x + 2.
Word Problems
Involving Linear
Equation in Two
Variables.
Sample Problems.
1. A taxi company charges a flat fee of
P30.00 for riding a taxi and an
additional P 25.00 per kilometer.
i. Write an equation to find the cost of a taxi ride.
Let x represent the number of kilometers and y
represent the total cost.
ii.How much is the cost of an 8-km taxi ride?
Solution
Representation:
x – number of kilometers
y – total cost
Equation:
y = 25x + 30
Solution: (cost of an 8 km taxi ride)
y = 25x + 30
y = 25(8) + 30
y = 200 + 30
y = P230
--------------Final Answer
2. The cost to take a taxi from the airport is a
linear equation of the distance driven. The cost
for 3, 6, and 12 km are shown in the table.
A. Write an equation in slope-intercept form
that represents the Equation.
B. How much is the cost of a 60 km ride?
Distance (km)
Cost (P)
3
14
6
23
12
41
Solution:
Representation:
x – number of kilometers
y – total cost
Equation:
y = 3x + 5
Solution: (Cost for a 60 km trip)
y = 3x + 5
y = 3(60) + 5
y = 180 + 5
y = P185
-----------------Final Answer
Try this!
A recording studio charges musicians an
initial fee of P5,000 to record an album.
Studio time costs an additional P3,500 per
hour.
a. Write an equation that gives the total cost
of an album as a function of studio time (in
hours)
b. Find the total cost of recording an album
that takes 10 hours of studio time.
Board Drill
The initial fee to have a website
set up using a server is P480. It
costs P440 per month to
maintain a website. What is the
total cost of setting up and
maintaining the website for 6
months?
Board Drill
The cost of renting a car
is P500 a day plus P20
per km travelled. Find the
cost of renting a car that
will be used for a 150 km
trip.
Board Drill
A taxi company charges a flat fee
of P45 for riding a taxi and an
additional P 30 per kilometer. How
much is the cost of an 20-mile taxi
ride?
The cost to take a taxi from the airport is a
linear equation of the distance driven. The cost
for 4, 8, and 16 km are shown in the table.
How much is the cost of a 80 km ride?
Distance (km)
Cost (P)
4
25
8
33
16
49
Board Drill
A