Algebra Unit 2 Review Linear Equations

Finding Slope

Today we'll be exploring how to find the slope of the line.

Learning target:

I can find the slope of a line on a grid.

There are multiple ways to find the slope of the line.

One way to find slope is by diving the vertical side by the horizontal side of slope triangles.

In this case

You can see that vertical length of the yellow triangle is 3 and the horizontal length is 4. To find the slope, you can divide 3 by 4 (which equals .75). Or you can write the slope as 3/4.

Another way to find slope is counting the rise over run.

Meaning, you can pick a plotted point and count how many squares it goes up and then how many it goes over until it hits the next point.

Watch the intro video on finding slope. Copy and paste the URL into a new tab. Be prepared to answer questions based on the video.

• https://www.youtube.com/watch?v=zihsQC0IUd8

Multiple Choice

What is the slope of the line?

• -2/3

• 3/2

• 2/3

• -3/2

Multiple Choice

What is the slope of the line?

• 2/3

• -2/3

• 3/2

• -3/2

Sometimes slopes will be undefined or have a slope of zero.

When a slope is in a completely straight horizontal line, then the slope is considered zero.

When a slope is in a completely straight vertical line, then the slope is considered undefined.

The slope of this line is zero

The slope of this line is undefined

Remember, a slope is positive when the staircase is going up.

The image to your right shows a positive slope.

Remember, a slope is negative when the staircase is upside down.

The image to your right shows a negative slope.

Don't forget that your slopes should be simplified.

If you have a slope of 10/5, it can be simplified to 2/1

Multiple Choice

What is the slope of the line?

• Undefined

• -1

• Zero

• 1

Fill in the Blanks

What is the slope of the line?

Multiple Select

What is the slope of the line?

*Select all answers that apply

• -1/3

• -3

• 1/3

• 3

Multiple Choice

What is the slope of the line?

• -1/2

• 1

• -1

• -2

Multiple Choice

What is the slope of the line?

• 3/2

• 2/3

• -3/2

• -2/3

Multiple Choice

What is the slope of the line?

• Zero

• Undefined

• -1

• 1

Fill in the Blanks

What is the slope of the line?

y=mx+b

Slope-intercept form is a format we use to write the equation of a line.

each letter represents something different

m = slope

b= y-intercept

y= all the y-coordinate values on the line

x= all the x-coordinate values

Multiple Choice

What does "b" represent in y=mx+b?

• slope

• y-intercept

• all the y-coordinate values on the line

• all the x-coordinate values on the line

Multiple Choice

What does "m" represent in y=mx+b?

• slope

• y-intercept

• all the y-coordinate values on the line

• all the x-coordinate values on the line

Identifying m & b in equations (y=mx+b)

• y= 4x - 3 ..... m= 4 , b= -3

• y = -3x + 7 ..... m= -3 , b= 7

• y = x - 8 ..... m= 1 , b= -8

• y = -x ..... m= -1 , b= 0

• y = 5x + 10 ..... m= 5 , b= 10

Multiple Choice

y = -7x +9

Identify the slope

• m= 9

• m=-7

• m= 7x

• m= -7x

Multiple Choice

y = -7x +9

Identify the y-intercept

• b= 9

• b=-7

• b= 7x

• b= -7x

Multiple Choice

y = -x -10

Identify the m & b

• m= -x , b= -10

• m= -x , b= 10

• m= -1 , b= -10

• m= -1 , b= 10

Slope

• a ratio that describes the steepness of a line

• 4 types of slope - positive, negation, zero, undefined

Multiple Choice

This slope is ...

• negative

• positive

• zero

• undefined

Multiple Choice

This slope is ...

• negative

• positive

• zero

• undefined

Multiple Choice

This slope is ...

• negative

• positive

• zero

• undefined

Finding Slope

• Find two points on the graphed line

• Find the change y over the change in x (rise over run).

Multiple Choice

The slope of the line is...

• 0

• 1

• -1

• - 1/1

Multiple Choice

The slope of the line is...

• 0

• 1

• -1

• - 1/1

Multiple Choice

The slope of the line is...

• 5/4

• -5/4

• -4/5

• 4/5

Slope from 2-points

Finding Slope when given 2 points.

Multiple Choice

Find the slope of the line that passes through:
(-2, 8) and (0, 8)

• 0
• -2
• 2
• 1/2

Multiple Choice

Find the slope of the line that passes through:
(10, 1) and (5, 2)

• 1/5
• -1/5
• 5
• -5

Multiple Choice

Find the slope given these points:

(2,-4) & (3,1)

• 5

• -3

• 3

• -5

Multiple Choice

Find the slope of the line that passes through:

(2, 4) and (6, 12)

• 1/2

• -1/2

• 2

• -2

Multiple Choice

Find the slope of the line that passes through:

(2, 4) and (6, 12)

• 1/2

• -1/2

• 2

• -2

Standard Form Equations: x & y intercepts

By Hannah Kilgore

What is an intercept?

• x-intercepts are where the line crosses the x-axis

• y-intercepts are where the line crosses the y-axis

Multiple Choice

^{What is the x- intercept of the line?}

• (1, 0)

• (2, 0)

• ( -1, 0)

• (-2, 0)

Multiple Choice

^{What is the y- intercept of the line?}

• (-1, -1)

• (2, 0)
• ( -1, 0)
• (-2, 0)

Multiple Choice

What is the y-intercept?

• (0,7)
• (0, 0)
• (0,1)
• (0, 2)

Multiple Choice

Give the y-interecept
3x + y = 5

• (-3, 0)
• (0,5)
• (5, 0)
• (0, -3)

Multiple Choice

Give the x-intercept
3x + 8y = 24

• (8, 0)
• (0, 8)
• (3, 0)
• (0, 3)

Multiple Choice

What is the x and y intercept for the following equation ?
4x - 10y = 20

• x - int = 4    
  y-int = -10
• x-int = 5
  y-int = 2
• x - int = 5
  y int = -2
• x -int = 4
  y -int = -10

Multiple Choice

Name the x- and y-intercepts for the equation:
2x + y = 6

• (0, 3) and (6, 0)

• (0, -3) and (-6, 0)

• (3, 0) and (0, 6)

• (-3, 0) and (0, -6)

Multiple Choice

What is the equation of the linear parent function?

• $$y=x$$  

• $$y=x^2$$  

• $$y=x^3$$  

• $$y=\sqrt[]{x}$$  

Multiple Choice

What is the Y-INTERCEPT of the linear parent function ?

• 1

• 2

• 0

• None

Multiple Choice

Compare $$y=x$$  and $$y=5x$$

• $$y=5x$$  is LESS STEEP than $$y=x$$  

• $$y=5x$$  is STEEPER than $$y=x$$  

• $$y=x$$ has the SAME slope as $$y=5x$$  

• $$y=x$$  is STEEPER than $$y=5x$$  

Multiple Choice

Compare $$y=x$$  and $$y=\frac{3}{2}x$$  

• $$y=\frac{3}{2}x$$  is STEEPER than $$y=x$$  

• $$y=x$$  is STEEPER than $$y=\frac{3}{2}x$$  

• $$y=\frac{3}{2}x$$  is LESS STEEP than $$y=x$$  

• $$y=x$$  has the SAME slope as $$y=\frac{3}{2}x$$  

Multiple Choice

Compare $$y=x$$  and $$y=\frac{1}{2}x$$  

• $$y=\frac{1}{2}x$$  is STEEPER than $$y=x$$  

• $$y=\frac{1}{2}x$$  is LESS STEEP than $$y=x$$  

• $$y=x$$  is STEEPER than $$y=\frac{1}{2}x$$  s

• $$y=x$$  has the SAME slope as $$y=\frac{1}{2}x$$  

Multiple Choice

Compare $$y=x$$  and $$y=x-1$$  

• $$y=x-1$$  is STEEPER than $$y=x$$  

• $$y=x-1$$  SHIFTED DOWN 1 unit from $$y=x$$  

• $$y=x-1$$  is LESS STEEP than $$y=x$$  

• $$y=x-1$$  SHIFTED UP 1 unit from $$y=x$$  

Multiple Choice

Compare $$y=x$$  and $$y=x+6$$  

• $$y=x+6$$  SHIFTED DOWN 6 units from $$y=x$$   

• $$y=x+6$$  is STEEPER than $$y=x$$  

• $$y=x+6$$  SHIFTED UP 6 units from $$y=x$$  

• $$y=x+6$$  is LESS STEEP than $$y=x$$  

Multiple Choice

The graphs of linear functions f(x) and g(x) are shown on the grid. Which function is best represented by the graph of g(x) ?

• $$g\left(x\right)=f\left(x\right)+3$$  

• $$g\left(x\right)=f\left(x\right)-3$$  

• $$g\left(x\right)=3f\left(x\right)$$  

• $$g\left(x\right)=-3f\left(x\right)$$  

Multiple Choice

The graphs of linear functions f(x) and g(x) are shown on the grid. Which function is best represented by the graph of g(x) ?

• $$g\left(x\right)=f\left(x\right)+4$$  

• $$g\left(x\right)=f\left(x\right)+5$$  

• $$g\left(x\right)=3f\left(x\right)$$  

• $$g\left(x\right)=\frac{1}{3}f\left(x\right)$$  

Multiple Choice

$$f\left(x\right)=x$$  and  $$g\left(x\right)=2x-4$$  

Which statement about the relationship of these two graphs is true?

• The graph of $$g\left(x\right)$$   is steeper than the graph of $$f\left(x\right)$$  , and the y-intercept has been translated up.

• The graph of $$g\left(x\right)$$ is less steep than the graph of $$f\left(x\right)$$  , and the y-intercept has been translated up

• The graph of $$g\left(x\right)$$   is less steep than the graph of $$f\left(x\right)$$  , and the y-intercept has been translated down.

• The graph of $$g\left(x\right)$$   is steeper than the graph of $$f\left(x\right)$$  , and the y-intercept has been translated down.

Multiple Choice

$$f\left(x\right)=x$$  and  $$g\left(x\right)=-\frac{2}{3}x$$  

Which statement about the relationship between these two graphs is true?

• The graph of g is less steep than the graph of f.

• The graph of g is less steep than the graph of f, and is reflected.

• The graph of g is reflected, and the y-intercept is translated down.

• The graph of g is steeper than the graph of f, and is reflected.