11.6 Slope

Rate of Change – identifies the relationship between two #’s that are changing Slope – a line’s rate of change Slope formula =

There are many ways to express slope: rise run change in y change in x vertical change horizontal change y 2 - y 1 x 2 - x 1

The variable m is used to represent slope…so

You can think of slope as the “steepness” factor The greater the slope, the steeper the line. Which line has a greater slope?

Let’s calculate it! (8,6) & (0,-1) are points on this line… (1,3) & (0,1) are points on this line…

The slope of a line CAN be negative…and you can tell just by looking at it!

The slope of a line CAN be negative…and you can tell just by looking at it or you can calculate it!! (-3,3) & (1,-3) are points on this line…

The slope of a line CAN be zero…and you can tell just by looking at it!

The slope of a line CAN be zero…and you can tell just by looking at it or you can calculate it. (0,-4) & (-2,-4) are points on this line… All horizontal lines have a zero slope.

The slope of a line CAN be undefined…and you can tell just by looking at it!

The slope of a line CAN be undefined…and you can tell just by looking at it or you can calculate it. (4,3) & (4,-6) are points on this line… All vertical lines have an undefined slope.

You can find the slope by “counting off” on the graph. You must go down 3 and 1 to the left to get to the next point. Down 3 = -3, and left 1 = -1, so the slope would be or just 3. If you start at this point You must go up 3 and 1 to the right to get to the next point. up 3 = 3, and right 1 = 1, so the slope would be or just 3.

It doesn’t matter which set of points you use to calculate the slope of a line. The entire line has the same slope…