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Practice with

y = mx + b

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Previously on MFM2P...

What is the equation of the following graph?

We need:

  • Slope

  • y intercept

​

Equation: y = -⅓ x -2

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Previously on MFM2P...

What is the equation of the following graph?

We need:

  • Slope

  • y intercept

​

Equation: y = 2 x +1

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Equation From a Graph

  • Identify the y-intercept
    • (spoiler: it happens the line crosses the y-axis)
  • Determine the slope
    • It’s the rise divided by the run
      • Find the rise between any 2 points, then find the run between the same 2 points and divide them.

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How Do We Use This Knowledge?

Rate of Change: _________

Slope: ________________

Initial Value: ____________

y-intercept: ____________

In words: The account balance starts at ____ and _______ by ___________

Equation:______________

y = mx + b form: __________

Account Balance ($)

Number of Weeks

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How Do We Use This Knowledge?

Equation: b = -50 + 30w

y = mx + b form: y = 30x - 50

After 6 weeks, how much money is in the account?

y = 30 (6) - 50

= 180 - 50

= 130

Therefore there is $130 in the account after 6 weeks.

Account Balance ($)

Number of Weeks

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How Do We Use This Knowledge?

Equation: b = -50 + 30w

y = mx + b form: y = 30x - 50

How many weeks does it take to reach $250?

250 = 30x - 50

250 + 50 = 30x - 50 + 50

300 = 30x

30 30

x = 10

Therefore it takes 10 weeks to reach $250.

Account Balance ($)

Number of Weeks

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From a Table?

Determining an equation from a table is similar to how we do it graphically:

  • Identify the y-intercept
    • (spoiler: it happens when x = 0)
  • Determine the slope
    • It’s the rise divided by the run
      • Find the rise between any 2 points, then find the run between the same 2 points and divide them.

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From a Table?

Here’s an Example

  • Identify the y-intercept

5

x

y

-5

15

0

5

5

-5

  • Determine the slope

-10

5

m= = -2

-10 5

Equation: y = -2x + 5

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Determine the Equation

x

y

-2

-5

-1

-3

0

-1

1

1

2

3

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Determine the Equation

x

y

-2

4

-1

0

0

-4

1

-8

2

-12

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Determine the Equation

x

y

-2

6

-1

12

0

18

1

24

2

30

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Determine the Equation

x

y

-2

15

-1

16.5

0

18

1

19.5

2

21

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Determine the Equation

x

y

-10

-23

-5

-8

0

7

5

22

10

37

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Determine the Equation

x

y

-5

23

-4

18

-3

13

-2

8

-1

3

0

​

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Determine the Equation

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Determine the Equation

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Determine the Equation

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Determine the Equation

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How Tall is the Door Frame?

You probably noticed that Mr. Rivard brought some styrofoam cups with him and didn’t tell you why.

How many cups will stack to the top of the door frame?

Yes. I know I didn’t bring enough cups to count.

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Determine the Equation (Challenge!)

Don’t worry if you can’t get this one