SlopeSpecial Section

SWBATUnderstand the meaning of the word slope

Find the slope using two points on a line

Determine the difference between positive slope, negative slope, zero slope

Show lines that have the same slope are parallel

Understanding SlopeSlope is the ratio of the vertical change to

the horziontal change

In other words: Slope is the steepness of a line

Mathematical Facts about Slope

Slope is denoted by the letter m

The vertical change (change in y) is called the rise

The horizontal change (change in x) is called the run

Mr. V, what are you talking

about?

Find the Slope by Counting

Find the Slope by Graphing:Find the slope of a line that goes through points (- 3, 5)

and (2,1)Plot the points

To solve by graphing:Start at the left dot and count down

till you’reeven with the right dot.

To solve by graphing: Now count over till you reach

the right dot.

Now SolveWe counted DOWN 4 spots, so we moved (– 4) units

We counted RIGHT 5 spots, so we moved 5 units

So our slope is:

m = - 4/5

Using Math to Find Slope

When given two points (x1, y1) and (x2, y2) you can find the slope of a line by using the following formula:

Slope Formula Continued

Example of a Negative Slope

GroupTry: Without graphing Find the Slope of a line through

points (2,1) and (4,4)

Remember:

Hint: Identify (x1, y1) and (x2, y2)

Group Try: Find the Slope of a line through

points (2,1) and (4,4)

Try on your ownFind the slope through the points (7, -4) and (9, 4)

Find the slope through the points (9, - 2) and (3, -5)

Answer: m = 4

Answer: m = - ½

Slope and Steepness

The greater the number, the steeper the slope (“faster” it moves up or down)

The smaller the number, the more gentle the slope (“slower” it moves up or down)

m = 4 >> m =1/4 >>

Classifying SlopePositive Slope – Slants up from left to right (“uphill”)

Negative Slope – Slants down from left to right (“downhill”)

Classifying SlopeZero Slope – Line is horizontal (driving an a flat road)

Undefined Slope – Line is vertical (straight up and down) – Can you drive a car up a wall? NO!

On Your Own:Label each slope as positive, negative,

zero slope, or undefined

One More Quick Note

Parallel lines have the same slope

In Your Group1) What is the slope of the line

represented by the table of values below?

Answer: m = 10

x y0 - 20 1 - 10 2 0 3 10

Which Graph has a Positive Slope?

A B

C D

A!!

Which statement best describes the slope of the line

graphed above?The slope is – 6

The slope is 2/3

The slope is 3/2

The slope is – 4

If you said: The slope is 2/3

You were WRONG!

The slope is 3/2

Which line has the greatest slope?

This Guy!!!

Ticket to LeaveWrite the slope formula using m, x1, y1, x2, y2

Find the slope of the line that passes through the points (-2, 5) and (4, -5)

Describe the difference between the graph of a line with a positive slope and a negative slope

Describe the difference between the graph of a line with zero slope and undefined slope