7-4 Scatter Plots

• Objectives: Graph and interpret points on scatter plots.

• Scatter plot– convey overall impression of relationship

between two variables

Study Hours Regents Score 3 80 5 90 2 75 6 80 7 90 1 50 2 65 7 85 1 40 7 100

•Note that with scatter plots, the points are not connected

Is the coloration positive, negative or neither?

7-5 Graphing linear equations

• Objectives: Graph linear equations by using the x and y intercepts or the slope and y intercept

• (Intercepts are the points where the line crosses the axes)

Since two points determine a line, we can use the intercepts to graph.

Graph the line 2x+4y=8

Set x to 0 and solve for y. 2(0)+4y=8

4y=8y=2

Now solve for x by setting y to 02x+4(0)=8

2x=8x=4

(0,2)

(4,0)

When the equation is in standard form (ax+by=c) complete the following:

• (Intercepts are the points where the line crosses the axes)

Since two points determine a line, we can use the intercepts to graph.

Graph the line 2x+4y=8

Plot the two points and draw a line running through the points

(0,2)

(4,0)

When equations are in slope intercept form :y=mx+b…

• Identify the y intercept by setting x to “0”

• Plot the y intercept

• Identify a second point by plotting the slope. You do this by starting at your y intercept point.

7-6 Families of Linear Graphs

• Objectives: Explore the effects of changing the slopes and y intercepts of linear functions

• Changing slopes

y=1/2x +2

y=2x+2

y=2/7x+2

As the slopes gets bigger, the number increases and the pitch gets steeper

As the slope gets smaller, the number decreases and the pitch becomes less steep

7-7 Parallel and perpendicular lines

• Objectives: Write an equation of a line that is parallel or perpendicular to the graph of a given equation and that passes through a given point.

Parallel lines are lines that will never touch or cross

•In each case the lines have the same slope

•The only difference between the 4 lines is where they cross the y line

y=1x+4

y=1x+3/2

y=1x

y=1x-3/2

• Perpendicular lines are lines that cross @ a right angle. The slopes are opposite reciprocals of each other.

y=2/1x+2

y=-1/2x-5/2

The slopes (m) have opposite signs

The rise/run has flipped

Chapter review• Given 4 points of a line find the slope of a line

•Given the slope of an equation and a point the line goes through, write the equation in point slope form

•Write equations of lines in slope intercept, Standard form, and point slope

The format dictates the process

If the equation is in slope intercept form (y=mx+b) identify the

yintercept and then plot the slope at lest two times to form your line

• The y intercept is -4

• From (0,-4) go down 3 and to the right 5 or

• From (0,-4) go up 3 and to the left 5

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y = −3

5x − 4

• If the equation is in standard form (ax+by=c):

• identify the y intercept by setting x to 0 and solve for x

• Then identify the x intercept by setting y to 0 and solve for x.

• Set x to 0

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−2x −3

2y = 6

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−2(0) −3

2y = 6

−3

2y = 6

−2

3= 6(−

2

3)

y = −12

3y = −4

(0, -4)

Set y to 0

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−2x −3

2(0) = 6

−2x = 6

−2

−2x =

6

−2x = −3

(-3,0)