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Writing Linear Equations

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Recall the four ways to find slope

• from a table

• from a graph

• from 2 points

• from an equation

Multiple Choice

Find the slope of a line that passes through the points (3, -5) and (6, -6)

• -1/3

• -3

• 1/3

• 3

Multiple Choice

Find the slope from the following equation.

 $y=\frac{3}{4}x+4$  

• 4

• 3/4

• I have no clue because I don't pay attention to Ms. Staggs

• What is slope?

Multiple Choice

Find the slope in simplest form

• 1/2

• -2

• 2

• 4/2

Multiple Choice

Find the slope in simplest form

• I have no clue how to do this

• 1/3

• 3

Recall the various linear equations

• point-slope

• slope-intercept

• standard

Multiple Choice

Identify the form of this linear equation

 $y=mx+b$  

• point-slope

• slope-intercept
  

• standard

Multiple Choice

Identify the form of this linear equation

 $y-y_1=m\left(x-x_1\right)$  

• point-slope

• slope-intercept
  

• standard

Writing linear equations

When writing linear equations, we want to use slope-intercept form (y=mx+b). There are different ways to do this depending on the information we are given.

Write a linear equation using points

• First find the slope

• Now pick one of those points

• Plug the slope (m) and the point (x₁, y₁) into the point-slope equation y-y₁=m(x-x₁)

• Simplify and reduce until you have the equation in slope-intercept form (y=mx+b)

Fill in the Blanks

Write a linear equation using the points (3, -5) and (6, -6). (type without any spaces)

Write a linear equation using a table

• pick two points from the table

• calculate the slope

• pick one point from the table

• plug in your slope and your point into the point-slope equation y-y₁=m(x-x₁) then simplify and reduce until the equation is in slope-intercept form (y=mx+b)

• If the y-intercept is included in the table, you can skip this step and just plug your slope and intercept into y=mx+b

Fill in the Blanks

Write the linear equation using the table provided. (Type without spaces)

Writing a linear equation given a graph

• Identify your slope by picking two points from the line and finding your RISE over RUN

• Identify where the line crosses the y-axis to find your y-intercept

• Plug information into y=mx+b

But Ms. Staggs, what if the graph doesn't show the y-intercept?

• You will need to pick ONE point from the line graphed

• Then use your slope and that point and plug into point-slope equation y-y₁=m(x-x₁)

• Simplify and reduce until in slope-intercept form y=mx+b

Fill in the Blanks

Using the following graphing, write a linear equation. (Type without spaces)

Poll

I understand how to write linear equations given two points, a table, and a graph

• Yes, I could do it on my own

• No, I would like additional help

Open Ended

What are some concepts you feel that you need more practice on next week before the test? Be specific so I can plan accordingly!

Solving Linear Equations

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PEMDAS

• Parenthesis (This means distribute and solve () first)

• Exponents (this includes square roots)

• Multiply or Divide next from left to right

• Add or Subtract next from left to right

Multiple Choice

Simplify:

63 ÷ 7 - 3 ⋅ 2 + 4

• 7

• -9

• -1

• 3

Multiple Choice

Simplify:

42 - 2 ⋅ (9 - 3) + 3

• 243

• 33

• 24

• 29

Multiple Choice

Simplify:

24 ÷ 4 ⋅ 2 + (3² - 1 + 6)

• 5

• 14

• 17

• 26

Opposite Operations

• Use Op Op when you don't know the variable.

• SADMEP

• Start furthest away from the variable.

• Get the variable on one side and numbers on the other.

Multiple Choice

What is the opposite operation of addition?

• subtraction

• multiplication

• division

• square root

Multiple Choice

What is the opposite operation of multiplication?

• addition

• subtraction

• division

• square root

Multiple Choice

What is the opposite operation of squaring a number?

• taking the square root

• dividing

• multiplying

• subtracting

Multiple Choice

How do you solve 9x - 4 = 23

• divide both sides by 4, then add 9

• add 4 to both sides, then divide both sides by 9

• divide both sides by 9, then add 4

• add 4 to both sides, then divide by 23

How to Solve for a Variable

• Check that the expression is simplified

• Distribute first

• Combine Like Terms

• Do Opposite Operations to get the Variable alone

Equations with variables on both sides: 20-7x=6x-6 (video) | Khan Academy

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Multiple Choice

The first step to solving the equation g - 3 = -12 is to . . .

• divide by -3 on both sides of the equal sign

• multiply by -3 on both sides of the equal sign

• subtract 3 on both sides of the equal sign

• add 3 on both sides of the equal sign

Multiple Choice

What is the first step in solving for w in the equation 3w + 5 = 14?

• Add 5 to both sides of the equal sign

• Divide by 3 on both sides of the equal sign

• Subtract 5 from both sides of the equal sign

• Multiply by 3 on both sides of the equal sign

Multiple Choice

19  + a  =  -50

• a = -950
• a =  -69
• a = -31
• a = -50/19

Multiple Choice

Solve the equation:
-5x = 25

• x = 20
• x = -20
• x = -5
• x = 5

Multiple Choice

3x - 5 = -26

• x=-21

• x=21

• x=-7

• x=61

Multiple Choice

Solve for x: 
4x + 1 = 7x - 5

• -1
• 2
• 6/11
• 8

Multiple Choice

Solve: -7(z - 6) = -70

• 16

• -16

• 8

• -1/2