Chapter 6: Graphing Lines by Elizabeth Niedland

Section 6-1: Rate of Change and Slope

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Rate of change: Allows you to see the relationship between two quantities that are

changing.

rate of change = change in the dependent variable / change in the independent variable

Section 6-2: Slope Intercept Form of a Line

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Linear Equations when graphed will ALWAYS be a straight line.

3 Forms of Linear Equations: Slope intercept, standard form, and point-slope form.

Slope Intercept

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y=mx+b

m: Slope, coefficient of x

b: y intercept (where the line intercepts the y axis)

Practice:

y=2x+1

Slope = ?

Y-intercept = ?

Graphing a Slope Intercept

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1.) Graph the y intercept

2.) Using the slope, find another point on your line

3.) Draw the line

Practice Problems:

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Solve for y and graph.

1.) 2y=4x+6

2.) 2y-6=3x

Counting Method

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What is the equation for this graph in slope intercept form?

When y/x is a Constant:

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When y = a constant ex. y=2, you will have a horizontal line at the y intercept.

When x = a constant ex. x=3, you will have a vertical line.

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Section 6-3: Applying Linear Functions

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You can use linear functions in real life situations!

Example From Textbook:

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Section 6-4: Standard Form

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

Steps to find the X and Y intercepts:

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1.) To find the x-intercept, plug in 0 for y and solve.

2.) To find the y-intercept plug in 0 for x and solve.

3.) Once both intercepts are found, plot as points.

Practice Problem: Standard Form --> Slope Intercept

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2x+3y=-12

3y=-2x-12

y= -2/3x+4

Slope = ?

Y-intercept = ?

Section 6-5: Point-Slope From and Writing Linear Equations

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y-y1=m(x-x1)

Example Problem:

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(2,3) (3,5)

y1-y2 / x1-x2 = 3-5/2-3 = 2/1 = 2

y-3=2(x-2)

This would be your answer if asked to put into point slope form.

Practice Problem: Write in Point Slope

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1.) (-2,3) ; m=4

2.) (5,-3) ; m=-2

Section 6-6: Parallel and Perpendicular Lines

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EVERY set of parallel lines will always have the same slope.

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Then, write in slope intercept and graph!

Are These Parallel Lines?

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1.) y=1/2x+1

y= 1/2x-3

2.)y=3/4-1

y=-3/4-1

Perpendicular Lines:

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- Lines are perpendicular if their slopes are the NEGATIVE RECIPROCAL of each other.

Ex. a/b, -b/a = perpendicular slopes

Are these Perpendicular Lines?

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1.) y=2/3x+1

y= -3/2+1

2.) y=2x+1

6x+3y=4

- Here, you would put both lines in slope intercept form!

Practice Problem: Graph

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1.) 3x-5y=15

2.)x+4y=4

Section 6-8: Graphing Absolute Values

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y= |x|

Chart would look like:

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Translation = shifting the graph horizontally or vertically.

Practice: Graph

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1.) y=|x+1|

2.)y=|x| + 1

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To get a vertical translation, the number will be outside of the absolute value bars. To get a horizontal translation, the number will be inside of the absolute value bars.

More Practice: Graph

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1.) y= |x| - 3

2.) y = |x - 2|

Works Cited

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Bellman, Allan E., et al. Algebra 1. Boston: Pearson/Prentice Hall, 2009. Print.

Niedland, Libby. "Chapter 6". Math Notebook: n. pag. Print.