slope & y-intercept edited version of kballard @ math.weebly.com

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slope & y- intercept Edited version of kballard @ math.weebly.com

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slope & y-intercept

Edited version of

kballard @ math.weebly.com

Vocabulary

• A rate of change is a ratio that compares the amount of change of a dependent variable to the independent variable.

• Slope: the steepness of a line described by rate of change of y and x.

Steepness of Lines

• The slope of a line is a measure of its steepness.• Use absolute value to compare the steepness of

multiple lines.

What is slope?

What does slope look like?

• There are four types of slope that describe the rate of change.

• Using this will help you check your work and describe your linear equation.

Slope Formula

• If you do not have a graph, but want to find the slope, you can use two points in the slope formula.

1)Substitute in both points2)Subtract and simplify

Slope-Intercept FormSlope-Intercept Form• The linear equation y = mx + by = mx + b is written in slope-

intercept form.

• x and y stand for any x and y value.

• mm is the slopeslope (rise over run)

• bb is the y-intercepty-intercept (on the y-axis)

y = mmx + bb

Identify slope and y-interceptIdentify slope and y-intercept

y= mx + by= mx + bmm is always slope

b b is always the y-intercept

Look at each equation and determine the slope value and the y-intercept value.

1)1) y = 4x + 5y = 4x + 5

2)2) y = ½ x – 7y = ½ x – 7

3)3) y = x – ¾ y = x – ¾

4)4) y = -x + 3y = -x + 3

5)5) y = x y = x

6)6) y = 4y = 4

7)7) x = 2x = 2

Identify slope and y-interceptIdentify slope and y-intercept

y = mx + by = mx + b

If you have the graph,1) Find the y-intercept2) Count rise over run3) Write the equation

Write the linear equation.Write the linear equation.

• Write the equation in slope-intercept form.• y = mx + b

Graphing a line.Graphing a line.• Slope-intercept form

is the easiest way to graph a line when you have an equation.• It is the main way that

lines are expressed.

Y = x + 2

Examples

Describing Slope -EX

• Tell whether the slope of each line is positive, negative, zero, or undefined.

Finding Slope from a Graph-Ex

• To find the slope from a graph,1)Pick any two points on the line.2)Count RISE over RUN and simplify

)(

)(

xRUN

yRISEm

Practice

• Name the type of slope and find the slope.

Special Cases

Practice

• Find the slope of each line.

Slope Formula-EX

Practice

Graph Lines #1Graph Lines #1• How will we graph a

line when we have y=mx + b?

Example: y = 2/3x - 4 m= _____ b = _______1) Plot the y-intercept2) Use your slope to count

rise over run3) Connect the dots!

Graph Lines #2Graph Lines #2

• How will we graph a line when we have y=mx + b?

Example: y = -3x + 2m= _____ b = _______1) Plot the y-intercept2) Use your slope to count

rise over run3) Connect the dots!

Graph Lines #3 Graph Lines #3 • How will we graph a

line when we have y=mx + b?

Example: y = 1m= _____ b = _______1) Plot the y-intercept2) Use your slope to count

rise over run3) Connect the dots!

Graph Lines #4Graph Lines #4• How will we graph a

line when we have y=mx + b?

Example: x = -3m= _____ b = _______1) Plot the y-intercept2) Use your slope to count

rise over run3) Connect the dots!

Graph LinesGraph Lines• Identify the slope and y-intercept,

then graph the linear equation.

1) y = 2x + 32) y = -½x - 13) y = 5/6x + 8

4) y = x - 7

REVIEW

1) What is rate of change?2) What is slope?3) What are the four types of slope?4) What does “rise” represent?5) What does “run” represent?6) How do you find slope from a graph?7) What is the slope formula?

Review1) What is slope-intercept form?

2) What do m and b represent?

3) How do you graph a line with slope-intercept form?

4) What are the two special cases?

MATH HUMOR• How are linear functions similar to Cupid? – They have a partner for every number.

• Teacher: Where’s the graph of your function?– Student: It was intercepted on the way to school.

• Why were the math students getting up and sprinting around the classroom?– Their teacher kept saing “rise” and “run”

• Why was the scientist smiling as he worked?– His graph had a great plot!