Calculating Slope

Calculating Slope

From Sequences, Tables, Graphs, Situations, Equations, and Points

Identifying Slope From an Equation

The variable "m" represents the slope in the equation y = mx + b. The slope will always be the number that precedes the "x" when an equation is written in slope intercept form (y = mx + b). The COEFFICIENT of "x" is the slope.

Multiple Choice

What is the slope in the equation y = 3x + 6?

• 3

• 6/3 = 2

• 3/6 = 1/2

• 6

Fill in the Blanks

What is the slope in the equations y = x + 7?

Multiple Choice

What is the slope in the equation y = x/3 - 2

• -2

• 3

• 1/3

• 2/3

Calculate Slope from Two Points

• Use the slope formula ^y2-y1/_x2-x1

• Remember to label one point as Point 1 and the other as Point 2. Label the x and y (x,y) from each point.

• Plug in the appropriate numbers to the formula and calculate the slope.

Multiple Choice

Calculate the slope of the line that goes through the following points: (0, 4) (6, 13)

• 9

• 3/2

• 2/3

• -3

Multiple Choice

Calculate the slope of the line that goes through the following points: (-2, 5) (1, -7)

• -4

• -2

• 12

• 3

Multiple Choice

Calculate the slope of the line that goes through the following points: (0,0) (2,4)

• 4

• -2

• 2

• 1/2

Calculating Slope From Graphs

• Use ^rise/_run to calculate slope from a graph.

• This is just counting the 'vertical change' and the 'horizontal change.'

• ^{Change in Y}/_{Change in X}

• Horizontal and Vertical Lines are special cases

Slope

-If the line is increasing from left to right, it has a POSITIVE slope.

-If the line is decreasing from left to right, it has a NEGATIVE slope.

-A horizontal line has a slope of ZERO (there is no 'rise,' but there is a 'run').

-A vertical line has an UNDEFINED slope because there is a 'rise,' but there is no 'run' and we cannot divide by zero (no zero in the denominator).

Multiple Choice

Use the graph to calculate the slope of the line.

• 3/2

• -3/2

• -3

• -2

Multiple Select

The slope of this line is...

• Zero

• Undefined

• Negative

• Positive

Multiple Select

The slope of this line is...

• Zero

• Undefined

• Negative

• Positive

Fill in the Blanks

The slope of a vertical line is...

Multiple Choice

• 3

• 2

• -6

• 1/3

Calculating Slope From a Table

• Remember to determine what is happening to the y-values, then the x-values.

• Write a ratio for each (especially if it is not consistent).

• Compare the ratios to make sure that they are equal and the rate of change is CONSTANT!

• ^{Change in Y}/_{Change in X}

Multiple Choice

Calculate the slope from the table:

• 10

• -10

• -20

• 2

Multiple Choice

Calculate the slope from the table:

• 8

• 2

• 4

• 1/4

Calculating Slope From a Sequence

• Remember to just identify the pattern!

• If you are adding or subtracting the same number each time, then your sequence is ARITHMETIC (Linear).

Multiple Choice

Calculate the slope (or common difference).

• -4

• 1/4

• 1

• 4

Fill in the Blanks

Calculate the slope (or common difference) of this sequence: -5, 4, 13, 22, 31, 40...

Calculating Slope From Situations

• Look for KEY words such as "each," "every," and "per."

• Remember that the slope is what is happneing every time (or what is happening over and over again)!

Multiple Choice

Calculate the slope of the line that represents this situation: The diver DESCENDS 5 feet every second.

• 5

• -5

• 1/5

• -1/5

Fill in the Blanks

Identify the slope of a line that represents this situation: The babysitter gets paid $8 each hour.

Multiple Select

The slope of this line is...

• Zero

• Undefined

• Negative

• Positive