Math 8 ( Period 1)

Chapter 3-2 Slope

Slope is the steepness of a line. The coefficient of the x term makes the slope steeper as it gets bigger.

4x is a steeper line than 3x, which is steeper than 2x
A fraction ( or decimal) coefficient makes the slope less than 45 degrees.

A 45 degree angle was a slope of 1 ( which actually is steep)

To make the line look like its going UP from left to right, the slope is POSITIVE
To make a line look like its going DOWN from left to right, the slope is NEGATIVE

There are several ways to think of slope to actually calculate it

Slope = rise/run ( rise over run)
=change in the y values/ change in the x values
=Difference of the y-values/ Difference of the x-values

Mrs Sobieraj uses “Be y’s first!” Be wise first! 
meaning always start with the y vales on top (in the numerator)

So Slope is the RATE OF CHANGE and  if it’s a CONSTANT rate of change, you have a LINEar relationship.

This slope, constant rate of change is the UNIT RATE in a real world problem.

TWO WAYS OF CALCULATING on a graph:

1  1)  pick 2 points and use the following formula
Difference of the 2 y –values/ Difference of the 2 x-values
The formal is restated with SUBSCRIPTS on the x’s and y’s below: (memorize this)

y₂ – y₁/ x₂-x₁  

The subscripts just differentiate between point one and point two. You get to decide which point is point one or two. I usually try to keep the difference positive, if I can—but often, one of them will be negative and the other will be positive.

EXAMPLE:   ( 3, 6)  and (2, 4)   
y₂ – y₁/ x₂-x₁     
6-4/3-2 = 2/1 = 2

   2)   Count the slope on the GRAPH using rise over run.
From the point (2,4) count the steps UP ( vertically) to (3,6): I get 2 steps
Now count how many steps over to the right (horizontally): 1 step
Rise = 2 and Run = 1 or 2/1 = 2