Rate of Change and Slope 11-18

 If you didn’t already turn it in…show me now!

 Determine the rate of change given a graph, a statement, or a table.  Determine the slope between two points on a line.

 Do the investigation in your groups. If you have questions – ask!

 When points on a graph make a line, a ratio like can be written as or This is called a rate of change.  Rate of change is also called the slope of a line. The rate of change (slope) is the change in y-value divided by the change in x-value.  We can find slope by looking at a graph and seeing how far we have to go up or down and how far we have to go over (left or right) to get from point to point.

 The slope of a line can be positive, negative, zero or undefined. Ski Bird is going to try to help you remember what each of these kinds of slopes looks like!  REMEMBER: SLOPE IS RATE OF CHANGE!!!

 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.

 Lines 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.

 Lines 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, and he is not trying to slow down. His energy level (and his enjoyment level) is at zero.

 Vertical 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 is to American as Gradient is to Cambridge!

 Find the slope of the lines. a. Slope = __________ b. Slope = ___________ y x y x

 Find the gradient of the line using the two points given. Then tell whether the slope is positive or negative. a. Gradient = ________ b. Gradient = _______ Positive or Negative Positive or Negative y x y x

 Find the slope of the lines. a. m = ___________b. m = _____________ y x y x

 How can you tell if a slope if positive, negative, zero, or undefined? ◦ Positive ◦ Negative ◦ Zero ◦ Undefined

 Place a point on the graph so that the line connecting your point and the point already on the graph has a slope of y x

HW: Practice Rate of Change and Slope Worksheet Begin your Sample Assessment!