Lesson 5-1Rate of Change and Slope

Sept. 8, 2014

Daily Learning Target

• I will find rates of change from tables

• I will calculate slope.

Slope is a measure ofSteepness.

Types of Slope

PositiveNegative

Zero

Undefinedor

No Slope

Slope is sometimesreferred to as the“rate of change”

between 2 points.

The letter “m” isused to represent

slope.

Why?

If given 2 points on a line, you may findthe slope using theformula y2 – y1

x2 – x1m =

The formula may sometimes be written

as m =∆y . ∆x

What is ∆ ?

Find the slope of the line through the

points (3,7) and (5, 19).x1 y1 x2 y2

m = 19 – 7

5 – 3 m = 12 2

m = 6

(3, 4) and (-6, -2)

-2 – 4 -6 – 3 m = -6 -9

m = ⅔

m=

Example 1

Time (min) Distance (ft)

1 260

2 520

3 780

4 1040

The following table shows the distance a band marches over time. Is the rate of change in distance with respect to time constant? What does the rate of change represent?

What if thenumerator is 0?

What if thedenominator is 0?

If given the graphof a line, find the

slope by using the“triangle” method to

find the rise over run.

rise = 4

run = 5

m= rise

run

m= 4/5

Homework

• Workbook

• page 139 problems 1, 3, 5, 6, 8, 12, 13, 15

• Page 141 1-6 ALL