Identifying Slope and Rate of Change

Slope and Rate of Change Lesson

(slope = rate of change)

Four Types of Slope

• Positive: up and to the right OR down and to the left

• Negative: up and to the left OR down and do the right

• Zero: no vertical change, horizontal line 

• Undefined: no horizontal change, vertical line

Slope on a Graph

More About Zero and Undefined Slopes

Horizontal Lines have zero slope. The rise between any two points on a horizontal run is 0, and 0 divided by any "run" is 0.

Vertical lines have an undefined slope. The rise between any two points on a vertical line can be counted, but the run will be zero. And any number divided by zero is undefined.

Multiple Choice

What is the slope of the line?

• $$m=\frac{3}{2}$$

• $$m\ =\ \frac{2}{3}$$

• $$m\ =\ -\frac{3}{2}$$

• $$m\ =\ -\frac{2}{3}$$

Multiple Choice

What is the slope of this line?

• Zero

• -2

• undefined

• 8

Slope from a Table

Multiple Choice

What is the slope shown on the table?

• m = -4

• m = $$\frac{2}{3}$$

• m = $$\frac{3}{2}$$

• m = $$-\frac{2}{3}$$

Slope from Two Ordered Pairs

Multiple Choice

Find the slope of the line that contains (3, -4) and (-1, 6)

• $$m\ =\ 1$$

• $$m=\frac{5}{2}$$

• $$m=-\frac{5}{2}$$

• $$m=-1$$

Slope/Rate of Change in Word Problems

• Marci travels 65 miles per hour

• Daniel earns $14 per hour

• Sheila bakes 3 cookies per person

• Ground beef costs $4.50 per pound

• ______per______ indicates a rate of change

• Could also be "each hat costs $14" or "car rental is $50 a day", etc.
  

Multiple Choice

Jack is running away from the Giant, and he has a pretty good head start.

After five seconds, he is 43 feet away from the Giant.

After ten seconds, Jack is 58 feet away.

Find the rate of change.

• 3 feet per second

• 5 feet per second

• 15 feet per second