1 What you will learn today 1. Review of slope 2. How to determine slope 3. How to graph a linear...

1

What you will learn today

1. Review of slope2. How to determine slope3. How to graph a linear equation in y = mx + b form4. Slopes of parallel and perpendicular lines5. How to graph a linear equation in standard form

Objective: 2.2 Slope and 2.3 Quick Graphs

2

Fun with Slope

Slope is the ratio of vertical change to horizontal change – rise over run.

x-10 -5 5 10

y

-10

-5

5

10


3

Finding Slope

1. Look at the graph and “count” the vertical change over the horizontal change.

2. Use the formula for finding slope:

Where you have two points (x1, y1) (x2, y2)

12

12

xx

yym


4

Finding Slope Using the Formula Example: Find the slope of a line passing

through(-3, 5) and (2, 1)


5

You Try Find the slope of the line passing through (-2, -4) and (3, -1)


6

Types of Slope

x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10

Positive m > 0 negative m<0 no slope m = 0

x-10 -5 5 10

y

-10

-5

5

10

Undefined slope


7

Classifying Lines Using Slope Example: Without graphing tell whether

the line through the given points rises, falls, is horizontal, or is vertical.a. (3, -4), (1, -6) b. (2, -1), (2, 5)


8

Comparing Steepness of Lines

Example: Tell which line is steeper:Line 1: through (2,3) and (4,7) or

Line 2: through (-1,2) and (4,5)


9

Parallel and Perpendicular Lines

Parallel lines have slopes that are equal.

Perpendicular lines have slopes that are the negative reciprocal of one another (e.g. 2 and -1/2)


10

Parallel or Perpendicular Example: Tell whether the lines are

parallel, perpendicular, or neither. a. Line 1 through (-3, 3) and (3, 1)

Line 2 through (-2,-3) and (2,3)

You Try: Line 1 through (1,-2) and (3,-2) Line 2 through (-5,4) and

(0,4)


11

Graphing Using the Slope-Intercept Form

y = mx + b is the slope intercept form of a linear equation.

b is the y-intercept (the place where the line crosses the y-axis)

m is the slope.


12

Steps for Graphing in Slope Intercept Form

1. Put the equation in slope-intercept form.

2. Find the y-intercept and use it to plot the point where the graph crosses the y-axis.

3. Find the slope in the equation and use it to “count” to a second point.

4. Draw a line through the two points


13

Example Graph y = 3/4x – 2 1. it is in slope intercept form. 2. y-intercept is -2 3. the slope is ¾ 4. connect the dots

x-10 -5 5 10

y

-10

-5

5

10


14

You Try Graph y = 1/2x + 1

x-10 -5 5 10

y

-10

-5

5

10


15

A Real World Example You are buying an $1100 computer on

layaway. You make a $250 deposit and then make weekly payments according the equation a = 850 – 50t where a is the amount you own and t is the number of weeks.

Step 1: rewrite as a = -50t + 850 Step 2: y-intercept is 850 Step 3: slope is -50 Step 4: connect the dots


16

Using the Standard Form to Graph an Equation

The standard form of a linear equation is Ax + By = C.

We will use the x and y intercepts to graph these types of equations.

x-10 -5 5 10

y

-10

-5

5

10


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The Steps

Step 1: Put the equation in standard formStep 2: Set y equal to zero and solve for x to get the x-intercept.Step 3: Set x equal to zero and solve for y to get the y-intercept.Step 4: Draw a line through the two points.


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Example Graph 2x + 3y = 12

x-10 -5 5 10

y

-10

-5

5

10


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Horizontal and Vertical Lines

The graph of y = some number is a horizontal line through (0, the number).

The graph of x = some number is a vertical line through (the number, 0).


20

Example Graph y = 3

Graph x = -2 x-10 -5 5 10

y

-10

-5

5

10


21

Homework Page 79, 18, 22, 24, 26, 27, 32-35 all,

41, 42, 44, 46 Page 86, 16-18 all,20, 26, 34, 37-39 all,

44, 52

1 What you will learn today 1. Review of slope 2. How to determine slope 3. How to graph a linear...

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