POD 7 Jan• Create a slope Circle Map

Slope

Definitions of Slope

• The tilt, inclination or steepness of a line

• The ratio of vertical change (rise) to horizontal change (run).

• The change in y (rise) over the change in x (run)

Tilt or Inclination

Vertical ChangeHorizontal Change

This ratio is also known as

Rise

Run

How many points do you need to draw a line?

• One

• Two

• Three

Graph (3,2) and (-1,-1)

Draw a line through the points.

Now that we have our line lets find its slope.

Remember we are finding the following ratio:Vertical or Rise

Horizontal Run

Vertical Change

or the Rise

3

Horizontal Changeor the Run

4

3

Vertical Rise Horizontal Run

3

4

Find the slope of the following line.

The slope is…

1

2

Find the slope of the line.

The slope is….

-3

Find the slope of these lines.

The slope is…

• Black line 3

• Red Line 1

• Blue Line -1/2

Find the slope of these lines

The slope is…

• Orange line 0

• Green Line Undefined

Slope InterceptReal Life Example 1

• Oranges from Florida cost $2 per pound. Let y represent the total cost and x represent the number of pounds of oranges. Create a table, then write a linear equation to find the total cost.

• Total cost = $2 times the number of pounds• y = 2x

Florida Oranges

• y = 2x• What is the

cost for 2 pounds?

• 10 pounds?

Slope InterceptReal Life Example 2

• Eileen’s limousine service charges a flat fee of $5 plus $10 per hour. Let y represent the total cost and x represent the number of hours. Write a linear equation to find the total cost.

• Total cost = $10 times the number of hours + flat fee

• y = 10x + 5

Eileen’s Limousine Service

• y = 10x + 5• What is the

cost for 1 hour?

• 4 hours?

Intercepts

y-intercept is the point the line meets the y-axis

y-intercept = 5

x-intercept is the point the line meets the x-axis

x-intercept = 7

Slope-Intercept Form

• Slope-intercept form of an equation assigns meaning to each variable.

• y = mx +b• In which m represents slope and b

represents your y-intercept.

Slope-intercept

y = mx + b

Slope y-intercept

Slope-Intercept Form

• To graph this equation first find and plot your y-intercept.

• Use your slope to locate a second point.• Lastly draw a line through your two points.

slope-intercept equation

. .

..

.

 

y-intercept (b) = -2