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3.1 Rectangular Coordinate System • Plot points on a rectangular coordinate system. • Determine whether ordered pairs are solutions of

equations. • Use the distance formula to find distance between two

points. • Us the midpoint formula to find the midpoints of line

segments.

Coordinate system – in our city

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• What are some of the solutions to this equation in two variable?

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Phones • The first minute of an international phone call is $0.96 and $0.75 for each additional minute. How will you find out a price of any phone call?

To represent relationships we use • 

min price

1 0.96

2 1.71

3 2.46

4 3.21

5 3.96

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Phone call min x

price y

1 0.96

2 1.71

3 2.46

4 3.21

5 3.96

Find the distance between the points. 1.  (4,-2) and (4,6)

2.  (-2,-2) and (4,-2)

3.  (4,6) and (-2,-2)

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Find the distance between the points. 1.  (x1,y2) and (x1,y1)

2.  (x2,y2) and (x1,y2)

3.  (x1,y1) and (x2,y2)

What is the distance between points (x1, y1) and (x2, y2) ?

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Find the midpoint of the line segment that joins the two points. 1.  (4,-1) and (10,3)

2.  (0,-5) and (2,-8)

3.2 Graphs of Equations • Sketch graphs of equations using the point-plotting

method. •  Find and use x-intercepts and y-intercept as aids to

sketching graphs.

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Find the x-intercept and y-intercept.

Sketch the graph of each equation.

What does the graph represent?

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3.3 Slope and Graphs of Linear Equations • Determine the slope of a line through two points. • Graph linear equations in slope-intercept form. • Use slopes to determine whether two lines are parallel,

perpendicular or neither. • Use slopes to describe rates of change in real-life

problems.

Find the slope of the line that passes through the given points.

1.  (2,-5) and (3,-5)

2.  (-3,4) and (-3,8)

3. 

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Sketch the graph of each line.

Which one has larger slope?

A B

1.  A 2.  B 3.  Neither. Their slopes are equal 4.  I am not able to tell

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Graph a line whose y-intercept is -2 and whose slope is 4/5.

€

A loading dock ramp rises 4 feet above the ground.

The ramp has a slope of 110

.

What is the hoizontal length of the ramp?

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Four pumps are emptying four different pools

Can two lines with positive slopes be perpendicular to each other?

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•  Parallel lines – two distinct lines are parallel if and only if they have the same slope

•  Perpendicular lines – two lines are perpendicular if and only if the product of their slopes is negative one (are opposite reciprocals of each other)

Which of the following lines are parallel? Which of the following lines are perpendicular?

Slope Rate of Change

€

m =change in ychange in x

=ΔyΔx

=y2 − y1

x2 − x1=

"rise""run"