3.3 Find Slope and 3.3 Find Slope and Rate of ChangeRate of Change

3.3 Find Slope and 3.3 Find Slope and Rate of ChangeRate of Change

Objective: Students will Objective: Students will be able to find the slope be able to find the slope of a line and interpret of a line and interpret

slope as a rate of changeslope as a rate of change

Definitions

• Slope- a ratio of the change in the y-coordinates to the change in the x-coordinates. Shows how steep a line is.

• Rate of Change- a ratio that describes how much one quantity changes with respect to a change in another quantity

Slope•Symbol “m”•m= Rise = change in y

Run Change in x

Form: m = y2- y1

x2 – x1

(x1,y1) , (x2,y2)

Find the Slope of the Line

Positive Slope

m › 0 line rises from left to right

y

x

Find the Slope of the Line

Negative Slope

m < 0 line falls

from left to right

y

x

Find the Slope of the line that passes

through the points

(-3,-1) and (2,-1)

Slope of Zero

m = 0 Horizonta

l Line

y

x

Find the slope of the line that passes

through the points

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

Undefined Slope

m = undefined

Vertical Line

y

x

List the 4 Ways we can classify the slope of a

Line

Positive

Negative No Slope

Undefined

Rate of Change

Rate of change = Change in y Change in x

Rate of ChangeUse the table to find the rate of

change. Then explain its meaning.

Number of

computer games

Total Cost(s)

x y

2 78

4 156

6 234

The table shows the cost of using a computer at an internet café for a given amount of time. Find the rate of change in cost with respect to time. Time (hours) 2 4 6

Cost (dollars) 7 14 21

Find the Rate of Change

Given the Slope find the missing coordinate

(x, 4), (6,-1); m= 5 6

Given the slope find the missing coordinate

(1,3), (9,y); m= 3

4

Given the Slope Find the Missing Coordinate

(4,3), (x,7) ; m= -2

(-4,r),(-8,3); m=-5