Slope


 * TASK: Describe slope in your own words (Look back at your flashcards if you need a hint).**

Slope is a number (a fraction, really) that tells us how steep or slanted a line is. More importantly, the slope of a line is like directions and it tells us how we move from one point to another on the line.
 * What is slope?**


 * How do we write slope?**
 * Slope is a fraction. The numerator of the fraction tells us how we move in the y-direction (up or down) to get from one point to another. The denominator of the fraction tells us how we move in the x-direction (left or right) to get from one point to another. **




 * How do we find slope?**
 * On the Regents, you may need to find the slope in one of two ways: from two given points or from a graph **

1. Finding Slope from a Graph:

//Example://

Since slope tells us how we move from one point to another on a line, the first thing we need to do it **find two points on the line**. In this example, two points are given to us. If they are not given to us, we can choose any two points we want.

Then, we need to find how we move up/down and left/right to get from one point to the other. We choose one point to start at (it doesn't matter which point you choose - either way you'll get the same slope) and count the spaces you have to move. For this example, we're going to start at point A and move to point B.


 * REMEMBER:** If you //move up//, the number is //positive//. If you //move down//, the number is //negative//. If you //move right//, the number is //positive//. If you //move// //left//, the number is //negative//.



From the diagram, we can see that the rise (or change in "y") is positive 4 and the run (or change in "x") is positive 8. Therefore, we can substitute those numbers into the slope formula and get:



Remember to always write your fraction in simplest form.

**TASK: Explain in your own words how you find slope from a graph.**

2. Finding Slope From Two Points:

Example:



For this type of slope problem, we're still trying to figure out how we move from one of these points to the other, but instead of graphing them and using the rise and run, we can use the last part of the slope formula that we didn't use above:



Note that the "y" direction (rise/up and down) still goes in the numerator and the "x" direction (run/left and right) still goes in the denominator.

We can choose one of the points to be Point 1 and be labelledand the other point will be Point 2 and will be labelled. It doesn't matter which point we choose to be point 1 and which to be point 2. We'll get the same slope either way. For this example, (3,4) will be point 1 and (-6, 10) will be point 2. Then, we can substitute the numbers from the points given into the formula:



**TASK: Explain in your own words how you find slope from two points.**

**TASK: Which method do you prefer? Why do you prefer this method?**

**TASK: Open the document below and complete the practice problems. Turn your worksheet in during class. **