Slope

Slope

These are some important vocabulary words we are going to learn about for our next unit

• Slope

• Proportionality

• Slope-Intercept Form

Today, we're going to focus on Slope

• This image is how you find the slope of a graph.

Multiple Choice

True or false: Slope is the same thing as Rate of Change

• True

• False

Slope = Rate of Change

• Slope shows you how much change there is between two points on a graph

• Slope and rate of change are the same thing.

This graph represents the function

y = x

You can also think of it as y = 1x We're going to look at this graph for the next few questions.

Open Ended

(Let's zoom in) What is the "change in y" from point A to point B?

Open Ended

What is the "change in x" from point A to point B?

Open Ended

What is the

 $\frac{change\ in\ y}{change\ in\ x}$  from point A to point B?

 $\frac{change\ in\ y}{change\ in\ x}\ =\ \frac{1}{1}$  

The slope of this graph is 1

This graph represents the function

y = 2x

We're going to look at this graph for the next few questions.

Open Ended

What is the "change in y" from point A to point B?

Open Ended

What is the "change in x" from point A to point B?

Open Ended

What is the

 $\frac{change\ in\ y}{change\ in\ x}$ from point A to point B?

Open Ended

What is the "change in y" from point A to point C?

Open Ended

What is the "change in x" from point A to point C?

Open Ended

What is the

 $\frac{change\ in\ y}{change\ in\ x}$  from point A to point C?

From point A to point B The slope is 2/1 From point A to point CThe slope is 4/2

Using any two points, The slope of this graph is 2

Multiple Choice

What is the slope for the equation y = 4x?

• 
  

  $\frac{1}{4}$
  

• $\frac{4}{1}$

• What is slope?

Multiple Choice

The slope of a graph is  $\frac{2}{5}$  What is the change in y from one point to the next?

• 
  

  2

• 5

• I need more info

Multiple Choice

What is the slope of this graph?

• 
  

   $\frac{1}{5}$  
  

•  $\frac{5}{1}$  

• I need more info

Slope

• Definition: How steep a line is. The amount of change between two points on a graph.

• Fact #1: In math, slope is represented by the letter m

• Fact #2: Slope is what you multiply times your input to get your output

Multiple Choice

What is the slope for the equation  $y=\frac{4}{9}x$  ?

• 
  

   $\frac{9}{4}$ 
  

•  $\frac{4}{9}$ 

•  $9$  
  

•  $4$  

Multiple Choice

What is the slope of this graph?

• 
  

   $m=3$  
  

•  $m=\frac{3}{1}$  

•  $m=\frac{1}{3}$  
  

Multiple Choice

What is the slope of this graph?

• 
  

   $m=\frac{2}{5}$  
  

•  $m=\frac{5}{2}$  

•  $m=2$  
  

Multiple Choice

What is the slope of this graph?

• 
  

   $m=\frac{2}{3}$  
  

•  $m=\frac{3}{2}$  

•  $m=2$  
  

•  $m=3$  

Multiple Choice

What is the slope of this graph?

• 
  

   $m=4$  
  

•  $m=\frac{1}{4}$  

•  $m=-\frac{1}{4}$  
  

•  $m=-4$  

Multiple Choice

If the slope is -4, What is the equation for the graph?

• 
  

   $y=4x$  
  

•  $y=-4x$  

•  $y=x-4$  
  

• How am I supposed to know that?

Great Job!