Transcript Parallel & Perpendicual Lines - Miami Beach Senior High School

Name:
Date:
Period:
Essential Question: 1. How can you determine if a line is parallel, perpendicular, or neither?
2. How can you determine whether two sets of data are related?
Topic: 1. Parallel & Perpendicular Lines
2. Scatter Plots & Trend Lines
Vocabulary:
Parallel Lines are lines in the same plane that do not
intersect and have the same slope.
y  mx  b
Slope-Intercept Form
•Useful for graphing since m is the slope and b is the y-intercept
y  y 1  m  x  x 1  Point-Slope Form
•Use this form when you know a point on the line and the slope
•Also can use this version if you have two points on the line
because you can first find the slope using the slope formula and
then use one of the points and the slope in this equation.
Ax  By  C
Standard Form
•Commonly used to write linear equation problems or express answers
*Reminder:
The slope is a number that tells "how steep" the line is and in which direction
Graphs of Parallel Lines
The red line is the graph of
y = – 4x – 3
and the blue line is the graph of
y = – 4x – 7
Testing if Lines are Parallel
Are the lines y = 3x – 4 and y = 3x + 8 parallel?
Are the lines y = 5x – 6 and y = 5x – 6 parallel?
Are the lines 12x + 3y = - 9 and -8x – 2y = 14 parallel?
Practice Testing if Lines are Parallel
1) y = - 2x – 4 and
y  
2) 4y = x + 5 and 12y – 3x = 2
1
2
x
2
3
Find the equation of a line going through the point (3, -5) and
parallel to y   2 x  8
3
3)
Find the equation of the line going through the point (4,1) and
parallel to y = - 3x + 7
Vocabulary:
Perpendicular Lines are lines in the same plane that
intersect at right angles and have opposite reciprocals slope.
Graphs of Perpendicular Lines
The red line is the graph of
y = – 2x + 5
and the blue line is the
graph of
y = 1/2 x +4
Finding Opposite Reciprocals
a)
b)
c)
d)
e)
f)
g)
h)
i)
-3
1/3
-2/5
6
-3/2
-1/6
8
3/8
7/3
Testing if Lines are Perpendicular
A re the lines 2 x  y  5 and y 
1
x  4 perpendicular?
2
Are the lines 6 x  3 y  5 and 2 y   4 x  4 perpendicular?
Practice Testing if Lines are Perpendicular
4)
Are the lines x  2 y  4 and 4 x  2 y  6 perpendicular?
Find the equation of a line going through the point (3, -5) and
perpendicular to y   2 x  8
3
5) Find the equation of the line going through the point (4,1) and
perpendicular to y = - 3x + 7
6) Find the equation of the line going through the point (-2,7) and
perpendicular to 2 x  y  8
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
y 
1
x2
5
y  5 x  1
perpendicular
Wrap-Up:
Quick Review:
Steps for determining if graphs are
parallel or perpendicular
1. Put both equations into slope-intercept form.
(Isolate for y ---- if ‘mx’ is on the side of the y move to the
other side, then divide everything by value in front of ‘y’)
2. Find the slope and y-intercept of each
equation.
3. Analyze the slope and y-intercept
Parallel – Slope is the same; y-intercept
different
Perpendicular – Slope is a opposite
reciprocal
Parallel Lines
Perpendicular
Lines
Independent Practice:
Page 330
(1-6)
VOCABULARY:
A scatter plot is a graph with points plotted to show a
possible relationship between two sets of data.
Ex: The table shows the number of cookies in a jar from
the time since they were baked. Graph a scatter plot using
the given data.
A correlation describes a relationship between two data sets. A
graph may show the correlation between data. The correlation can
help you analyze trends and make predictions. There are three
types of correlations between data.
It is often helpful to add a line to better describe a scatter plot.
This line, called a trend line, helps show the correlation
between data sets more clearly. It can also be helpful when
making predictions based on the data. An accurate trend line
should fit the data closely. There should be about the same
number of points above the line as below it.
How do I write an equation?
Slope
Point Slope
Practice:
a. Graph the (ages, grades) data of some
students in a school.
b. Draw a trend line.
c. Find the equation of the line of best fit.
Wrap-Up:
Fraction Review
Vocabulary Review
Home-Learning Assignment #5
3 fraction problems (assigned in class)
Page 331 (8, 14, 16, 18, 20)
Page 337 (1, 2)
•Summary