Slope

Slope

Today we will be looking at types of slope and how to find slope from a graph, from a table and from two point using the slope formula, and from equations both standard and slope-intercept form.

Types of slope

There are four main types of slope

=Positive Slope

=Negative Slope

=Zero Slope(y= line)

=Undefined Slope(x= line)

Multiple Choice

What type of slope is shown by the stairs in the image?

• positive

• negative

• undefined

• zero

Multiple Choice

What type of slope is shown in the image?

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

What type of slope is Mario running in the picture?

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

• Positive
• Zero
• Negative
• Undefined

Multiple Choice

• positive slope

• negative slope

• undefined (no) slope

• zero slope

Multiple Choice

• positive slope

• negative slope

• undefined (no) slope

• zero slope

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

• Negative
• Zero
• Undefined
• Positi

What does slope measure?

• Slope measures the steepness of a line.

• There are many ways to find slope.

• You can find slope by using the rise over the run on a graph.

• You can use the m-value from slope-intercept form (y=mx+b)

• You can use two points and calculate the slope using slope formula 

•  $m=\frac{y2-y1}{\text{x2-x1}}$  

Multiple Choice

When using a graph to find slope, which do you do first?

• Rise

• Run

Multiple Choice

The 'rise' in rise/run tells us which way to go on which axis?

• y-axis

• x-axis

• coordinate plane

• y-intercept

Multiple Choice

What direction do you go when you are finding the rise?

• left and right

• up and down

Multiple Choice

The 'run' in rise/run tells us which directions to go on the x-axis?

• up and down

• diagonal

• left and right

Multiple Choice

What is the slope of this line?

• 5/2

• 2/5

• -2/5

• -5/2

Multiple Choice

What is the slope of the line?

• 2/3

• -3/2

• 3/2

• -2/3

To find the slope of a line from a table

- Choose two points
        ex: (0,5) and (3,7)
-Use the slope formula

 $m=\frac{y2-y1}{x2-x1}$  

 $m=\frac{7-5}{3-0}$   
        7-5 =2, 3-0=3
  $m=\frac{2}{3}$  

Multiple Choice

What is the slope?

• 3
• -3
• 10
• -6

Multiple Choice

Find the rate of change shown in the table.

• -1.5 cm/week

• 1.5 cm/week

• -1/5 cm/week

• 1/5 cm/week

Multiple Choice

Find the rate of change shown in the table.

• 3/125

• 125/3

• 500/12

• -3/125

Multiple Choice

Find the average rate of change shown in the table above.

• -3 degrees F every 2 hours.

• -1.5 degrees F every hour.

• 3 degrees F every 2 hours.

• 1.5 degrees F every hour.

Finding slope from two point:

 - Label one point (x1, y1) and the other point (x2, y2)
- Use the slope formula: $m=\frac{y2-y1}{x2-x1}$  

- Simplify your answer to find the slope.

Multiple Choice

Determine the slope.

• m=1/7
• m=-1/7
• m=-7
• m=7

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:
(-12, -5) and (0, -8)

• 1/4
• -1/4
• 4
• -4

Multiple Choice

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

• 1/5
• -1/5
• 5
• -5

Identifying Slope from an Equation

Slope intercept form of an equation: y=mx+b

m=slope

b=y-intercept

Slope is always attached to the x value when in slope intercept form of a line

Multiple Choice

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

• y-intercept
• slope
• macaroni
• nothing

Multiple Choice

What is the slope in the equation:  y=4x+3

• 3
• 4x
• 4
• x

Multiple Choice

Which of these represents slope-intercept form?

• y - y₁ = m(x-x₁)

• Ax + By = C

• y = mx + b

Multiple Choice

What is the slope of the line with the equation
 $y\ =\ -\frac{3}{2}x\ +\ 4$  

•  $-\frac{3}{2}$  

•  $\frac{3}{2}$  

•  $4$  

•  $-4$  

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2
• 3
• 5
• Cannot be Determined 

Parallel Lines

Parallel lines are lines that have the exact same slope but different y-intercepts.

If the y-intercepts were the same, you would have the exact same line not parallel lines.

Multiple Choice

The slopes of parallel lines are...

• the same

• opposite

• always different

Multiple Choice

What slope is parallel to:  
m = ³/₄

• ⁴/₃
• ³/₄
• ^-3/₄
• ^-4/₃

Multiple Choice

Which line is parallel to
y = 2x - 7  ?

• y = -2x + 8
• y = ¹/₂x - 7 
• y = ^-1/₂x + 2
• y = 2x - 3 

Multiple Choice

y = 3x +2
y = 3x - 3
These lines are...

• Parallel
• Perpendicular
• Neither
• The same line

Perpendicular Lines

Perpendicular lines are lines that have slopes that are opposite recipricols of each other.

- opposite - signs change

- recipriols - position of the numbers change

ex: 3 and -1/3 are perpendicular slopes

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals.
• opposites.
• the same.
• always 7.

Multiple Choice

What is the slope of a line perpendicular to a line with slope ^-6/₅ ?

• ^-6/₅
• ^-5/6
• ⁵/₆
• ^-4/₃

Multiple Choice

Which line is perpendicular to
y = 2x - 7  ?

• y = -2x + 8
• y = ¹/₂x - 7 
• y = ^-1/₂x + 2
• y = 2x - 3 

Multiple Choice

y = ^{- 2}/₃x + 2
y = ³/₂x + 9
These lines are...

• Parallel
• Perpendicular
• Neither