8.4 Slope

Slope

​

Slope from an equation

• The number in front of the x in the equation is the slope!

Multiple Choice

In the equation y=mx+b, what does the m represent?

• slope

• y-intercept

• linear

• point-slope

Multiple Choice

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

• y-intercept

• macaroni

• nothing

• slope

Fill in the Blanks

$y=x+5$  

Identify the slope in the equation:

Multiple Choice

$$y=-\frac{4}{5}x-2$$  Identify the slope of the equation.

• 6

• $$\frac{4}{5}$$

• $$-\frac{4}{5}x$$

• $$-\frac{4}{5}$$

Multiple Choice

Identify the slope from the equation y = -8x

• m = -8

• m = 8

• m = x

• m = -8x

Multiple Choice

Identify the slope from the equations y = -x -6

• m = 6

• m = -1

• m = -x

Multiple Choice

Identify the slope and y-intercept...change to SIF first:

$$6x+3y=12$$  

• m = 6; b = 12
  

• m = 3; b = 4
  

• m = -2; b = 4
  

• m = 2; b = 4
  

Multiple Choice

Determine the slope and y-intercept (change to SIF):   4x + y = -10

• slope: 4

    y-intercept:  (0,10)

• slope: -4  

  y-intercept:  (0,-10)

• slope: -4  

  y-intercept:  (0,10)

• slope: 4

    y-intercept:  (0,-10)

Multiple Choice

What is the y-intercept of the line with the equation $$y\ =\ -2x\ +\ 4$$  

• $$-2$$  

• $$2$$  

• $$4$$  

• $$-4$$  

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6

• y=3x-6

• y=3x+6

• y=6x+3

Identifying Slope of a Line

• Slope can tell us the direction of the line!

• Refresh yourself of the 4 types of slope using the picture to the right:

Finding the Slope of a Line

• Slope can tell us how steep a line is!

• Each line can be assigned a value (a #) that tells us how steep the line is.

• Slope is written as a ratio (rise/run)

• Always make sure to simplify your answer! Pay attention to if the line is positive or negative

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{5}{3}$$  

• $$\frac{3}{5}$$  

• 5

• $$\frac{5}{4}$$  

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  

• $$\frac{2}{1}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{2}{3}$$

• $$\frac{3}{2}$$

• 3

• $$\frac{1}{3}$$

Multiple Choice

Find the slope

• -5/3

• -3/5

• 5/3

• 3/5

Multiple Choice

What type of slope?

• undefined

• positive slope

• negative slope

• zero slope

Multiple Choice

What type of slope?

• negative

• steep

• undefined

• zero slope

Multiple Choice

Which graph represents this slope and y-intercept $$y\ =\ -\frac{2}{3}x\ +\ 4$$  

Slope can be expressed in different ways:

What is the slope of a line between (-4,14) and (-16,8)?

Multiple Choice

Find the slope of the line that passes through:

(6,7) and (4,2)

• 2/5

• -5/2

• 5/2

• -1/2

Multiple Choice

Find the slope of the line that passes through:

(2, 4) and (6, 12)

• 1/2

• -1/2

• 2

• -2

Fill in the Blanks

What is the slope of a line between (-4,14) and (-16,8)? Reminder! 

Formula:

$m=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}$  

Multiple Choice

Find the slope of the line that passes through:

(-3, -4) and (7, 6)

• 0

• Undefined

• -1

• 1

Multiple Choice

Find the slope of the line that passes through:

(10, 1) and (5, 2)

• 1/5

• -1/5

• 5

• -5

What is the slope of a vertical line?

What is the slope of a horizontal line?

Negative slope

- A line has a negative slope if it is going downhill from left to right

Positive slope

- A line has a positive slope if it is going uphill from left to right

Poll

What do you think is the slope of a Vertical Line?

• 0

• Undefined

• 1

• -1

Poll

What do you think is the slope of a Horizontal Line?

• 0

• Undefined

• 1

• -1

Finding slope from a Table

• Slope = change in y/change in x

• Use the table to find the value the y is changing by. That is the numerator!

• Use the table to find the value the x is changing by. That is the denominator!

• ANOTHER OPTION: Graph the points and count rise/run

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

• $$2\ \frac{1}{2}$$

• 2

Multiple Choice

What is the slope of this table?

• 10

• 1/10

• 12

• 100

Multiple Choice

What is the slope of this table?

• 3/3

• 2/3

• 3/4

• 3/6

Multiple Choice

What is the slope of this table?

• 4/1

• 8/1

• 1/4

• 2/8

Multiple Choice

What is the slope of this table?

• 4/1

• 8/1

• 1/4

• 2/8

Open Ended

From what you think or know, what is a slope?