Slope

Ski Bird is going to try to help you remember how slope applies to straight

lines.

change in y overchange in x.

Slope is defined as…

 

riserun

What is rise?The rise is the vertical change that occurs on the y-axis. If it goes up, it is positive. If it goes down, it is negative.

What is run?The run is horizontal change that occurs on the x-axis. It runs from left to right. If it goes left, it is negative. If it goes right, it is positive.

Positive Slope

Lines that have positive slope, slant "up hill"(as viewed from left to right).Ski Bird has to work hard to make it up the hill. He needs to exert more positive (+) energy to get up the hill.

Negative SlopeLines that have negative slope, slant “down hill”(as viewed from left to right).Ski Bird enjoys the ride down the hill. He needs to decrease (-) energy to try to slow down.

Zero SlopeLines that are horizontal have zero slope.Ski Bird is cross-country skiing on level ground. He is not working hard to get up a hill, nor is he trying to slow down. His energy level (and his enjoyment level) is at zero.

No slopeVertical lines have no slope, or undefined slope.Ski Bird cannot ski vertically. Sheer doom awaits Ski Bird at the bottom of a vertical hill.

Slope can be expressed different ways:

A line has a positive slope if it is going uphill from left to right.

A line has a negative slope if it isgoing downhill from left to right.

2 1

2 1

( ) vertical change

( ) horizontal change

y y risem

x x run

When given the graph, it is easier to apply “rise over run”.

1) Determine the slope of the line.

Start with the lower point and count how much you rise and run to get to the other

point!

Determine the slope of the line.

6

3

run36

= =1

2

rise

Notice the slope is positive AND the line increases!