Slope is also know as the rate of change. Many real-world careers use rate of change:

(Finance, Interest rates,

anything with money)

Slope is found through ratios which are very important to statistics

Understanding slope and knowing how to calculate it is used in jobs such as Architecture, Construction, (anything involving building)

Even Athletics such as Cycling,

Skateboarding

Snowboarding

**SLOPE**

The meaning of Slope

Slope is:

the ratio of the change in the y-coordinates (rise) to the change in the x-coordinates (run) as you move from one point to another.

OR

m(slope)= rise

run

OR

• Change in Y (∆Y ) divided by change in X (∆X) Will see ∆ a lot in science class or advanced math.

(∆Y )

∆X

Possible Slopes

Positive: Y-increases as X-Increases

Negative: Y-decreases as X-Increases

Zero: Y is constant as X changes

Undefined: As Y changes X is constant

Goals

Understand the concept of slope

Calculate the slope: given two points, the graph of a line, or the equation of a line

Interpret the rate of change/slope and intercepts within the context of everyday life

How to find slope?

There are several ways to find slope.

Each way depends on what you know...

Two points

If you know any two points on a graph then you can find the slope.

Make a Triangle

With two known points on the graph can create a triangle.

The hypotenuse is the line

Each leg is either the vertical (rise) or horizontal (run)

Can’t create a triangle then the slope is either zero, undefined or not a linear function

Can find the slope by the length of the vertical side (rise) over the length of the horizontal side (run).

Using the equation:

Example:

If the graph of the line is shown on a coordinate plane designate any two points

Then count "up (down) and over (left or right)" till hit another part of the line

(Must run through coordinate where the x and y values are whole numbers to work)

Amount "UP or DOWN" on the graph DIVIDED by how many you went over (LEFT or RIGHT) will tell the SLOPE

Graph

Why Learn Slope?

Real World Problem

Jimbo's Roofin' Company is building the roofs for the new houses in a subdivision. They need to make sure that the slope of their roofs meet the county's building code which states that a roof can not have a slope steeper than 7/12. See if based upon the measurements whether or not each roof will pass inspection.

Geoboards

Groups of 3-4

Worksheet with group

If I see you using the rubber bands as anything other than making your slope then you will not be allowed to use the Boards anymore and will work alone to complete the assignment

.

Your Board should have the X and Y axis bars on them, and a pin is in the center holding them in place.

You should have all 4 quadrants of the XY plane graph.

Each hole represents a point on the graph.

Use the pegs to mark your points and the rubber band to connect them and create the slope.

Find the slope and draw the graph with the points and line:

1. (1, -5) (-4, 7)

2. (-5, -4) (4, -3)

3. (-3, -3) (1, 6)

What do you know about Common Difference?

What about Rate of change?

What about Proportions/Ratios?

What can you tell me about Slope?

Table

y2= ?

y1= ?

x2= ?

x1= ?

m=

m=

-2

2

-1

2

2-(-2) = 4

2-(-1) = 3

4/3

-4

+1

2

8

X

Y

2

5

5

-3

8

-11

Find the slope between each of these points

+3

-8

-8

m=-8/3

+3

Slope? Pass or Fail?

Roof #1: 24 ft long by 14 ft high

Roof #2: 16 ft long by 26 ft high

Roof #3: points on blueprint (-7,0) (4,5)

What type Slope is it?

1. (5, 12) ( 8, 16)

2. (-2, 8) (-6, 8)

3. (3,4) (7,1)

4. (3,18) (3, 21)

5. (-2, -6) (6, 8)

Possible Slopes (Arms)

1. Left arm up, right down

2. Left straight, right straight horizontal

3. Right up, left down

4. Right straight up, Left straight down

5. Right down, left up

Interactive Geoboard Website:

http://www.mathlearningcenter.org/web-apps/geoboard/

These are all related to and found in similar ways to SLOPE.

LINE

(x1, y1)

(x2, y2)

http://www.mathlearningcenter.org/web-apps/geoboard/

7/12

Pass

13/8

Fail

5/11

Pass