EXPLORING Mountains have slopes…. …and so do lines.

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Presentation transcript:

EXPLORING

Mountains have slopes….

…and so do lines.

A skier can go down this slope

When you think of down, you think of negative. This line, like the mountain, has a negative slope

You can also run up the mountain.

When you think of up, you think positive. This line, like the mountain, has a positive slope.

Does this mountain have a slope?? Slope?? This has zero slope!

Horizontal lines have a slope of zero. 000

What do you think the slope of a vertical line would be ?? This is not a slope; it’s a cliff! The slope of a vertical line is undefined! It has NO slope.

A line that goes down from left to right has what kind of slope???

A line that goes up from left to right has what kind of slope???

What kind of line has a slope of zero??

What is the slope of this line??

One more time… undefined

+ - 0 Matching. a. b. c. d.

Determining the Value of a Slope

Now that you can identify whether a line has a positive or negative slope, let’s learn how to determine the value of the slope. This line has a slope of 1. How do you figure that out?

First, a few facts about slope. Slope is the ratio of the change in y to the change in x. Vertical change : y _______________ Horizontal change : x Or in easy terms, it is RISE divided by RUN. RISE RUN Slope is always represented by the letter m

Look at your line and identify two points between which you can determine the slope. What is the rise? up 2 What is the run? over 2 This gives you the ratio: 

Let’s try another one. Choose two points. Count your rise. up 2 Count your run. over 3 So the slope is: 2 3

This one is a little different. Choose two points. Count your rise. up 1 Up 1 or +1 Count your run. back 2 Back 2 or -2 The slope is:  1 2  1 2 

To summarize… If you can count, you can find the slope. 1. Choose two points on the line. 2. Count from the lower point in a vertical direction to where the upper point is. 3. Count right or left to the second point. 4. The slope is the RISE (first distance) divided by the RUN (second distance).

Now it’s time for you to practice what you have learned!