Slope by Counting Foundations of Algebra

What is slope? What do you think of when you hear the term, slope? Do you think of a skier, skiing down a large mountain? Or, maybe you think of the sliding board at the playground. Whatever you are thinking, it's probably something that's on an incline!

What is the meaning of this sign? 1.Icy Road Ahead 2.Steep Road Ahead 3.Curvy Road Ahead 4.Trucks Entering Highway Ahead

What does the 7% mean? 7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally. 7% So, what is slope??? Slope is the steepness of a line. 7 feet 100 feet

How do you find slope? The slope of a line can be found in several different ways. You can use a line that already exists and you can count the slope OR you can use points on a graph and can plug them into a formula without even seeing the line!

The Steepness of a Line A line can be drawn in many different ways… A line can go up from left to right A line can go down from left to right A line can be flat A line can be straight up and down A line can go up really fast A line can go up slowly... All of these will effect a line’s SLOPE.

How to find slope by counting: Take any line that is plotted on the coordinate plane Find two points on the line. Count the rise (How many units do you count up or down to get from one point to the next?) This number is your numerator. Count the run (How many units do you count left or right to get to the point?) This number is your denominator. Simplify your fraction if possible.

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 run 3 6 == rise Notice the slope is positive AND the line increases!

2) Determine the slope of the line shown ½ 3.½ 4.2

What is the slope of a horizontal line? The line doesn’t rise! All horizontal lines have a slope of 0.

What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope.

Find the slope of the given lines.

Does it matter what points I pick?

What if there aren’t any points?

Review: Slope A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right. A line has a slope of zero if it is horizontal. A line has an undefined slope if it is vertical.