Slope of a Line

Slope of a Line

Slope

• Slope measures the steepness of a line

• Known as rate of change

• Known as rise over run

• Know as change in y over change in x

• Slope is represented by the variable "m"

Finding the Slope from Two Points

• Slope formula: (y₂- y₁ ) / (x ₂ - x₁ )

• Each point in the coordinate plane can be represented as an ordered pair (x, y)

• Label each set of points as (x , y ) and (x , y ). 

• To find the slope, subtract the y-values and divide by the difference of the x-values

Slope from Two Points in a Table

• Subtract y-values = numerator

• Subtract corresponding x-values = denominator

• Always reduce slope (simplifying the fraction)

Multiple Choice

What is the slope?

• 5
• 1/5
• 15
• 10

Multiple Choice

What is the slope?

• 2/5
• 5/2
• 3
• 5.5

Multiple Choice

What is the slope?

• -21
• -17
• 1/4
• 4

Multiple Choice

What is the slope?

• -1/3
• -3
• -4
• 5

Slope from Two Points on a Graph

• Locate two points on the line and determine the coordinates of each point (x, y)

• Label one point as (x ₁ , y ₁) and the other (x ₂ , y₂ )

• Use the slope formula to find the slope (y ₂- y₁)/ (x ₂- x₁)

Multiple Choice

What is the slope of the line?

• $\frac{1}{2}$

• 2

• -2

• $-\frac{1}{2}$

Multiple Choice

What is the slope of the line?

• -3

• -1

• 1

• 2

Multiple Choice

What is the slope of the line?

• $\frac{1}{2}$

• $2$

• $-\frac{1}{2}$

• -2

Slope from Graph (rise over run)

• Locate an anchor point - try to find one that is exactly on the intersection of a grid

• Locate a "destination" point - try to find one that is exactly on the intersection of a grid

• Count the units up or down from your anchor point to the destination point : up is positive and down is negative. This is your rise (numerator)

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Slope from Graph

• Count the units to the right or left from your anchor point to your destination point: right is positive, left is negative. this is your denominator

• anchor point (1, 4)

• destination point (4,2)

• Go down 2 (= -2) to the right 3 (=+3)

• Slope is -2/3

Multiple Choice

Find the slope of the line.

• 4/2

• -4/2

• 2/1

• -2/1

Multiple Choice

Find the slope of the line.

• -2/1

• 2/1

• -1/2

• 1/2

Multiple Choice

Find the slope of the line.

• 1/4

• -1/4

• -4/1

• 4/1

Multiple Choice

Find the slope of the line.

• 1/2

• -1/2

• 2/1

• -2/1

Slope from Slope-Intercept Form

• Slope intercept: y = mx + b

• m = slope; b = y-intercept

• The slope is always the coefficient of the x-term

• y = 5x - 4; slope = 5

• y = -1/2 x; slope = -1/2

• y = 5; no x-term so coefficient must be 0; slope = 0

Multiple Choice

What is the slope of y = 3x - 4

• 3

• -3

• 4

• -4

Multiple Choice

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

• 3

• 4x

• 4

• x

Multiple Choice

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

• 3

• 4x

• 4

• x

Slope and Rate of Change

• Slope and Rate of Change mean the same

• Usually we refer to slope when we talk about the slant of a linear function, and rate of change refers to the change between points in all types of functions

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Slope and Rate of Change

• Slope also refers to the line, while rate of change makes more sense when we talk about how the dependent variable changes with respect to the dependent variable

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Multiple Choice

During a snowstorm, John measured the total snowfall accumulated at the end of each hour.  He recorded his results in the table below.  What is the approximate average rate of change of the snowfall between 1 p.m. and 6 p.m.?

• 0.7 inch/hour
• 0.9 inch/hour
• 1.1 inch/hour
• 1.4 inch/hour

Multiple Choice

Find the rate of change.

• -2 minutes per gallon

• -20 minutes per gallon

• -2 gallons per minute

• -20 gallons per minute

Multiple Choice

Find the rate of change.

• -2 minutes per gallon

• -20 minutes per gallon

• -2 gallons per minute

• -20 gallons per minute