Rate of Change

SLOPE

AKA

Types of

Slopes

Negative SlopeLines that have negative slopes “slant downhill” as viewed from left to right.

Zero SlopeHorizontal lines have Zero “slant” or SLOPE.

Positive SlopeLines that have positive slopes “slant uphill” as viewed from left to right.

No SlopeVertical lines have NO SLOPE or an Undefined Slope

We find Slope/Rate of change in various ways.

Method 1: By finding the Rise over the Run, typically used when finding the slope/rate of change of a graph.

Method 2: By finding the change in y values divided by the change in x values , typically used when finding the slope or rate of change in a table of data.

Method 3: By using the slope formula , typically used when given two points from a line.

2 1

2 1

y yx x

Let’s Explore!

Slope AKA Rate of Change is the measurement of steepness

of a straight line.

x

y

Finding Slope /Rate of Change on a GRAPH

x

y

1. Pick two points anywhere on the line.2. Count how many units you have to “rise” to get from the 1st point to the 2nd point.

+ 3 3. Count how many units you have to “run” to get to the 2nd point.

+ 3

4. The slope/rate of change is the rise divided by the run.

Rise

Run

+3 +3

Rate of change or slope is +1

Now it’s your turn, complete Finding

Slope/Rate of Change from

graphs.

Finding Slope /Rate of Change from a TABLEx y-3 40 23 06 -29 -4

1. Find the change in the y values.

-2

-2

-2

-2

2. Find the change in the x values.

+3

+3

+3

+3

3. The slope/rate of change is the change in y divided by the change in x.

23m

Now it’s your turn, complete Finding

Slope/Rate of Change from tables.

Finding Slope /Rate of Change when given 2 POINTS.

What is “m” the slope of the line that contains the points (-2, 6) and ( -6, 7)?

Let’s explore 2 methods!

Finding Slope /Rate of Change when given 2 POINTS.

Method 1: Using the Slope formula

2 1

2 1

y yx xm =

Finding Slope /Rate of Change when given 2 POINTS.

Method 1: Slope formula

2 1

2 1

y yx x

m =

(-2, 6) and ( -6, 7)1. Label the points (x1,y1) and (x2,y2).

x1 x2y1 y2

2. Plug in to the formula and solve.

m =

2 1

2 1

y yx x7 6

-6 -2 14m

Finding Slope /Rate of Change when given 2 POINTS.

Method 2: Graph the points and use rise/run. (-2, 6) and ( -6, 7)

x

y

-1+4

RiseRun 4

-1

14m

Now it’s your turn, complete Finding

Slope/Rate of Change from given

points.