Patterns and Equations

Patterns, Slopes and Equations

What is the trend?

Multiple Choice

What is the slope trend here?

• Positive

• Negative

• Zero

• Undefined

POSITIVE Slope

LOOK LEFT TO RIGHT

POSITIVE - Goes UP or Increases Left to Right

Multiple Choice

What is the slope trend here?

• Positive

• Negative

• Zero

• Undefined

NEGATIVE Slope

Goes DOWN or Decreases Left to Right

Multiple Choice

What is the slope trend here?

• Positive

• Negative

• Zero

• Undefined

ZERO Slope

ZERO - NO Increase or Decrease. No Change

Multiple Choice

What is the slope trend here?

• Positive

• Negative

• Zero

• Undefined

UNDEFINED Slope

Undefined slope increases and decreases at the same time

This makes no sense so it's UNDEFINED

Multiple Choice

What is the slope?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What is the slope?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What is the slope?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What is the slope?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What is the slope?

• Positive

• Negative

• Zero

• Undefined

Find Slope on the Graph

Slope is Rise Over the Run

Open Ended

What is the RISE for this Line?

Open Ended

What is the RUN for this Line?

Multiple Choice

If the RISE is -3 and the RUN is +4, then what is the slope?

Remember: RISE OVER RUN

• $$-\frac{3}{4}$$

• $$-\frac{4}{3}$$

• $$-3$$  

• $$-34$$  

Multiple Choice

What is the slope?

• $$\frac{4}{3}$$

• $$\frac{3}{4}$$

• $$-\frac{4}{3}$$

• $$-\frac{3}{4}$$

Multiple Choice

What is the slope?

• $$2$$  
  

• $$0$$  
  

• $$3$$

• Undefined

Multiple Choice

What is the slope?

• $$\frac{1}{2}$$  
  

• $$\frac{2}{1}$$  
  

• $$1$$

• $$-\frac{1}{2}$$  
  

Multiple Choice

What is the slope?

• UNDEFINED

• $$0$$

• $$1$$

• $$-2$$

What is the equation? 

You need Two things

• m which is the SLOPE 

• b which is the Y-Intercept

Multiple Choice

What is the slope

• $$\frac{1}{2}$$

• $$\frac{2}{1}$$

• $$-\frac{1}{2}$$

Multiple Choice

What is the y-intercept?

• $$2$$

• $$1$$

• $$-4$$

Multiple Choice

What is the equation?

• $$y=\frac{1}{2}x+2$$

• $$y=2x+\frac{1}{2}$$

• $$\frac{1}{2}x+2$$

• $$y=\frac{1}{2}+2$$  

Multiple Choice

What is the equation?

• $$y=\frac{4}{3}x+4$$

• $$y=4x+\frac{4}{3}$$

• $$y=\frac{3}{4}x+4$$

Tile Patterns

Looking for a Pattern

Open Ended

How much are tile increasing or growing by?

Count the Growth between Figures

Multiple Choice

How much are the tiles increasing or growing by?

• Adding 4

• Adding 5

• Adding 3

• Adding 6

Multiple Choice

What's the increase or growth here?

• +1

• +2

• +3

• +4

What's the Equation?

You need Two Things

• m = SLOPE 

• b = Starting Point or Y-intercept

• b comes from Figure 0 not Figure 1

What's the Equation?

You need Two Things

• m = SLOPE = 2

• b = Starting Point or Y-intercept = 3

• b comes from Figure 0 not Figure 1

Open Ended

What is the equation? Type in as y = mx + b

Multiple Choice

What is the growth?

• +2

• +3

Multiple Choice

What is the Starting Point or b?

• 1

• 2

• 3

• 4

FIGURE 0 is the "b"

Multiple Choice

What is the equation?

• $$y=2x+1$$

• $$y=1x+2$$

• $$y=\frac{1}{2}x+1$$

• $$y=2x$$

Multiple Choice

What is the equation?

• $$y=4x+1$$

• $$y=1x+4$$

• $$y=\frac{1}{4}x+1$$

• $$y=4x$$

m = 4 and b =1

Don't forget Figure 0

Equation and Pattern in a Table

• A pattern can also be expressed in a table

• Input and Outputs have different ways you can label them

• Remember that the stating point (also called b or Y-intercept still comes from Figure 0 or where x = 0

Multiple Choice

What is the growth or pattern?

• add 2

• add 3

• add 4

Multiple Choice

What is the b or starting point

• 7

• 4

• 10

Remember the b comes from Figure 0 or where x = 0

Open Ended

What is the equation?

Multiple Choice

What the growth or pattern?

• add 2

• add 3

• add 4

• add 5

Multiple Choice

What is the b or y-intercept?

• 5

• 1

• 4

• 2

Multiple Choice

What is the equation?

• $$y=4x+1$$

• $$y=1x+4$$
  

• $$y=4+1$$
  

• $$4x+1$$

y = mx + b

m is the pattern and b is the starting point

m is first, b is last in the equation

Multiple Choice

What is the m or growth?

• add 3

• add 2

• add 4

• add 1

Multiple Choice

What is the b or y-intercept?

• -1

• -2

• 0

• 2

b = -1

 2 minus 3 = -1

Open Ended

What is the equation?

Multiple Choice

What is the pattern or m?

• +5

• -5

• +4

• -4

Multiple Choice

What is the b or starting point?

• 9

• 4

• 14

• -1

Multiple Choice

What is the equation?

• $$y=-5x+9$$

• $$y=9x+5$$

• $$y=5x+9$$

• $$y=-5x+14$$