classroom assignment

Slope and Rates of Change

Essential Questions

• How can I determine the steepness of a line?

• How can I represent the slope on a coordinate plane?

Georgia Performance Standard

• GA-GPS.M7A3: Students will understand relations and functions.

• GA-GPS.M7A3(b): Represent, describe and analyze a functional relation from a table, graph, and/or formula.

• GA-GPS.M7A3(c): Describe the variation of two quantities

SLOPE• Is a measurement of a line’s

steepness• Ratio of rise to run

x

Run

RiseRise

• line points upward as x increases, its slope is positive

• line points downward as x increases, its slope is negative

Positive

0

y

x

Negative Neither

Example 1Tell whether the slope is positive or negative. Then find the slope.

3

3

slope = riserun

= 33

= 1

Example 2Tell whether the slope is positive or negative. Then find the slope.

2

-3

0 2

2

–2–2

y

x

slope = riserun

= 2 -3

Example 3

M(1, –1) N(3, –1)

2

Tell whether the slope is positive or negative. Then find the slope.

slope = riserun

= 02

= 0

Example 4

(0, –4)

(–2, 4)

8

–2

slope = 8–2 = –4

Tell whether the slope is positive or negative. Then find the slope.

Negative.

Example 5You can graph a line if you know its

slope and one of its points.Use the slope - and the point (1, –1) to graph the line.

2 1

y

x–4

–4

4

4

0 2

2

–2–2

= orriserun

-2 1

2-1

●

●

• The ratio of two quantities that change, such as slope, is a rate of change.

• A constant rate of change describes changes of the same amount during equal intervals. The graph of a constant rate of change is a line.

• A variable rate of change describes changes of a different amount during equal intervals. the graph of a variable rate of change is not a line.

Example 7

Tell whether each graph shows a constant or variable rate of change.

A. B.

The graph is nonlinear,so the rate of change is variable.

The graph is linear, so the rate of change isconstant.

Example 8Tell whether each graph shows a constant or variable rate of change.

A. B.

The graph is nonlinear,so the rate of change is variable.

The graph is linear, so the rate of change isconstant.

y

x–4

–4

4

4

0 2

2

–2–2

y

x–4

–4

4

4

0 2

2

–2–2

Tell Whether the graphs are variable or constant

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

Constant or Variable

AssessmentSlope Poetry

• Students will create a poem that explains the rise over run relationship

• Include an illustration with your poem