Graphing Linear Equations

Graphing Linear Equations

Graphs and functions are critical, not only for solving math problems, but for real life situations. They can be used, for example, to find trends in data. None of this is possible, however, without first knowing the basic foundation of graphing, the different forms that an equation can be written in, or how to write these equations. These basics will be used for all types of more complex graphing in the future.

BIG PICTURE

Vocabulary

Slope: A ratio of the distance moved vertically over the distance moved horizontally in a non-vertical line.

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​y-Intercept: The point where a line crosses the y-axis

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Slope-Intercept Form: A form of writing a linear equation in two variables: y = mx+b, where m is the slope, b is they-intercept, and x and y are the variables.

Multiple Choice

In the equation y=mx+b,
what does m represent?

• Nothing in particular
• The y-intercept
• The x-intercept
• Slope

Multiple Choice

Name the slope

• 3
• 1
• -1x
• -1

Multiple Choice

Name the y intercept

• -1
• 7
• -1x
• -7

Multiple Choice

Name the y intercept

• 4
• -1
• 1
• -4

Multiple Choice

Name the slope

• 2
• -2
• 1/2
• 1/2x

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6
• y=3x-6
• y=3x+6
• y=6x+3

Open Ended

How are you feeling about Linear Equations so far?

(Respond with a complete).

Multiple Choice

Name the slope

• 3
• Zero slope
• Undefined
• 1

Multiple Choice

Name the slope

• Negative
• 0 Slope
• Undefined
• Positive

Multiple Choice

Name the slope

• 7/1
• 3/4
• -3/4
• -7/1

Multiple Choice

Name the slope.

• Zero slope
• 1
• Undefined
• -1

Multiple Choice

What is the equation of this line?

• y = 2x +2
• y = 2x -2
• y = -x + 2
• Cannot be Determined

Multiple Choice

Write the equation of the line.

• $$-2$$  

• $$2$$  

• $$4$$  

• $$-4$$  

Multiple Choice

Write the equation of the line.

• $$-2$$  

• $$2$$  

• $$4$$  

• $$-4$$  

Multiple Choice

What is the y-intercept of the line with the equation $$y\ =\ -2x\ +\ 4$$  

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$y=\frac{1}{2}x-4$$

• $$y=-\frac{1}{2}x-4$$

Multiple Choice

Write the equation of the graph in slope-intercept form

• $$-2$$  

• $$2$$  

• $$4$$  

• $$-4$$  

Multiple Choice

Which of these represents slope-intercept form?

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$y=\frac{1}{2}x-4$$

• $$y=-\frac{1}{2}x-4$$

Fill in the Blank

Write the slope intercept form of a line.

Multiple Choice

Find the slope of the following equation.  (Hint: Get y alone first)
3x-6y=12

• 3
• -3
• -1/2
• 1/2

Multiple Choice

WHAT HAPPENS WHEN m IS NEGATIVE?

• THE GRAPH GETS STEEPER.

• THE GRAPH IS INCREASING.

• THE GRAPH IS DECREASING.

• THE GRAPH IS FLATTER.

Multiple Choice

• PURPLE

• BLUE

• RED

• GREEN

Multiple Choice

Multiple Choice

Multiple Choice

Multiple Choice

Multiple Choice

Multiple Choice

Find the equation of the line that passes through the points:

(2, 2) and (3, 4)

• y = 2x + 2
• y = -2x - 2
• y = -2x + 2
• y = 2x - 2

Multiple Choice

Find the equation of the line that passes through the points:

(3, 4) and (0, -5)

• y = 3x + 5
• y = -3x + 4
• y = -3x + 4
• y = 3x - 5

Multiple Choice

Find the equation of the line that passes through the points:

(-3, 3) and (3, -1)

• y = -⅔ x + 1 
• y = -⅔ x  
• y = ⅔ x + 1 
• y = -⅔ x +3 

Multiple Choice

Find the equation of the line that passes through the points:
(0, -2) and (-5, 3)

• y = -x - 2
• y = x - 2
• y = x + 3
• y = -x - 3

Multiple Choice

Find the equation of the line that passes through the points:
(4, -1) and (0, -3)

• y = 2x - 3
• y = -2x + 3
• y = ½ x - 3
• y = -½ x + 3

Multiple Choice

Find the equation of the line that passes through the points:
(3, 3) and (1, -5)

• y = -9x + 4
• y = 4x - 9
• y = ¼ x + 9
• y = -9x - 4

Multiple Choice

Write a linear equation in the form of y=mx+b

• y= 3x + 5

• y = 5x - 3

• y = 2x + 3

• y = 5x + 3

Multiple Choice

Write a linear equation in the form of y=mx+b

• y = 2x + 2

• y = 2x - 2

• y = x + 2

• y = 3x - 2

Multiple Choice

Write a linear equation in the form of y=mx+b

• y = 3x - 3

• y = -3x + 3

• y = -3x - 3

• y = 3x + 3

Multiple Choice

Write a linear equation in the form of y=mx+b

• y = 3x + 5

• y = 2x + 5

• y = 5x - 2

• y = -3x + 5

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Multiple Choice

Write in slope intercept form
5x - 3y = -9

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$y=\frac{1}{2}x-4$$

• $$y=-\frac{1}{2}x-4$$

Multiple Choice

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$y=\frac{1}{2}x-4$$

• $$y=-\frac{1}{2}x-4$$

Multiple Choice

Write the equation in slope-intercept form:
-3y + 5x = 12

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$y=\frac{1}{2}x-4$$

• $$y=-\frac{1}{2}x-4$$

Multiple Choice

Write in slope intercept form
5x - 3y = -9

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$y=\frac{1}{2}x-4$$

• $$y=-\frac{1}{2}x-4$$

Multiple Choice

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$y=-\frac{1}{2}x-4$$

Multiple Choice

What is the slope intercept form of the equation
4x - 8y = 72

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$4$$  

• $$y=-\frac{1}{2}x-4$$

Multiple Choice

Write the equation in slope-intercept form:
-3y + 5x = 12

• y = -4 + 5x
• $$2$$  

• $$4$$  

• $$-4$$  

Multiple Choice

• 3

• $$2$$  

• $$4$$  

• $$-4$$  

Multiple Choice

Write in slope intercept form
5x - 3y = -9

• y = (5/3)x - 3
• y = (5/3)x + 9
• y = (5/3)x + 3
• $$-4$$  

Multiple Choice

Write the equation in slope-intercept form:
-3y + 5x = 12

• y = -4 + 5x
• y = -4 + 5/3x
• y = 4 - 5/3x
• $$y=-\frac{1}{2}x-4$$

Multiple Choice

• -1

• $$-\frac{1}{2}$$  

• $$-\frac{3}{2}$$  

• $$y=-\frac{1}{2}x-4$$

Open Ended

Write 3 ways to find the slope of a linear equation.

(Use complete sentences).