Topic: 1. Parallel & Perpendicular Lines

2. Scatter Plots & Trend Lines

Name:Date: Period:Essential Question:

Vocabulary:

Parallel Lines are lines in the same plane that do not intersect and have the same slope.

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?

bmxy Slope-Intercept Form

•Useful for graphing since m is the slope and b is the y-intercept

11 xxmyy 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.

CByAx Standard Form

•Commonly used to write linear equation problems or express answers

The slope is a number that tells "how steep" the line is and in which direction*Reminder:

Graphs of Parallel Lines

The red line is the graph of y = – 4x – 3 and the blue line is the graph ofy = – 4x – 7

Testing if Lines are Parallel

Are the lines 12x + 3y = - 9 and -8x – 2y = 14 parallel?

Are the lines y = 3x – 4 and y = 3x + 8 parallel?

Are the lines y = 5x – 6 and y = 5x – 6 parallel?

Practice Testing if Lines are Parallel

1) y = - 2x – 4 and 3

2

2

1 xy

2) 4y = x + 5 and 12y – 3x = 2

Find the equation of a line going through the point (3, -5) and parallel to 8

3

2 xy

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 thatintersect 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 ofy = 1/2 x +4

Finding Opposite Reciprocals

a) -3b) 1/3c) -2/5d) 6e) -3/2f) -1/6g) 8h) 3/8i) 7/3

Testing if Lines are Perpendicular

1Are the lines 2 5 and 4 perpendicular?

2x y y x

Are the lines 6 3 5 and 2 4 4 perpendicular?x y y x

Practice Testing if Lines are Perpendicular

Are the lines 2 4 and 4 2 6 perpendicular?x y x y 4)

Find the equation of a line going through the point (3, -5) and perpendicular to 2 83y x

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 8x y

From the given equations, determine if the corresponding lines are parallel, perpendicular, or neither.

y = 2x + 2y = 4x - 2

2x + 6y = 14x + 12y =3

15

25

1

xy

xy

neither

perpendicular

parallel

Quick Review:Steps for determining if graphs are

parallel or perpendicular1. Put both equations into slope-intercept form.

(Isolate for y ---- if ‘mx’ is on the side of the y move to theother 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-interceptParallel – Slope is the same; y-intercept differentPerpendicular – Slope is a opposite reciprocal

Wrap-Up:

Parallel Lines

Perpendicular Lines

Independent Practice:

Page 330(1-6)

A scatter plot is a graph with points plotted to show a possible relationship between two sets of data.

VOCABULARY:

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

•Summary

Home-Learning Assignment #53 fraction problems (assigned in class)

Page 331 (8, 14, 16, 18, 20)Page 337 (1, 2)