do now 10/29/09 copy hw in your planner. text page 239, #4-32 even in your notebook, answer the...
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Do Now 10/29/09
Copy HW in your planner.Text page 239, #4-32 even
In your notebook, answer the following question. There are two skateboard ramps at a skate park. One ramp is 12 ft long and 6 ft tall. The other is 10 ft long and 8 ft tall. Which ramp do you think is steeper? How can you tell?
Objective
SWBAT find the slope of a line and interpret slope as a rate of change
Section 4.4 “Section 4.4 “Find Slope and Rate Find Slope and Rate of Changeof Change””
SLOPE-SLOPE-the ratio of the vertical change (the rise) to the ratio of the vertical change (the rise) to the horizontal change (the run) between the horizontal change (the run) between any two points on a line.any two points on a line.
Slope = Slope = rise rise = = change in ychange in y run change in xrun change in x
Slope SymbolsSlope Symbols
The slope m of a line passing through two points
and is the ratio of the rise change to the run.
),( 11 yx ),( 22 yx
m
y
x
),( 11 yx
),( 22 yx
runrun
riserise)( 12 yy
)( 12 xx
“positive slope”
Slope SymbolsSlope Symbols
The slope m of a line passing through two points
and is the ratio of the rise change to the run.
),( 11 yx ),( 22 yx
m
y
x
),( 11 yx
),( 22 yxrunrun
riserise)( 12 yy
)( 12 xx “negative slope”
Find a positive slope
Let (x1, y1) = (–4, 2) = (x2, y2) = (2, 6).
m =y2 – y1
x2 – x1
6 – 22 – (– 4)
=
=46
23= Simplify.
Substitute.
Write formula for slope.
Find the slope of the line shown.
Let (x1, y1) = (5, 2) = (x2, y2) = (4, – 1).
m =y2 – y1
x2 – x1
(– 1) – 24 – 5
=
=– 3–1
= 3 Simplify.
Substitute.
Write formula for slope.
Find the slope of the line that passes through the points. (5, 2) and (4, –1)
XAMPLE 2Find a negative slope
Find the slope of the line shown.
m =y2 – y1
x2 – x1
Let (x1, y1) = (3, 5) and (x2, y2) = (6, –1).
–1 – 56 – 3
=
– 63= = –2
Write formula for slope.
Substitute.
Simplify.
(0, 6) and (5, –4)
m =y2 – y1
x2 – x1
Let (x1, y1) = (0, 6) and (x2, y2) = (5, – 4).
– 4 – 6 5 – 0
=
Write formula for slope.
Substitute.
Simplify. 10
5= – = – 2
Find the slope of the line that passes through the points
Find the slope of a horizontal and vertical lineFind the slope of the line shown.
Let (x1, y1) = (– 2, 4) and (x2, y2) = (4, 4).
m =
y2 – y1
x2 – x1
4 – 4
4 – (– 2)=
0
6= = 0
Write formula for slope.
Substitute.
Simplify.
EXAMPLE 4Find the slope of the line shown.
Let (x1, y1) = (3, 5) and (x2, y2) = (3, 1).
m =
y2 – y1
x2 – x1Write formula for slope.
1 – 5
3 – 3= Substitute.
Division by zero is undefined.– 4
0=
Identifying SlopesIdentifying Slopesm =
y2 – y1
x2 – x1Positive slopePositive slope
Negative slopeNegative slope
Slope of 0Slope of 0
UndefinedUndefined
Rate of Change
A rate of changerate of change compares a change in one quantity to change in another quantity.
Example: hourly wageExample: hourly wage
A rate of change describes how pay A rate of change describes how pay increases with respect to time spent working.increases with respect to time spent working.
The table shows the cost of using a computer at an Internet cafe 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
Rate of change =change in costchange in time
14 –74 – 2
=72= 3.5=
The rate of change in cost is $3.50 per hour.
Time(minute) 30 60 90
Distance (miles)
1.5 3 4.5
The table shows the distance a person walks for exercise. Find the rate of change in distance with respect to time.
Rate of changeRate of change ==change in distancechange in distance
change in timechange in time
33 – – 1.51.56060 – – 3030
== == 0.05 0.05ANSWER
The rate of change in distance is 0.05 mile/minute.
Section 4.4 “Slopes of Lines”Section 4.4 “Slopes of Lines”
How can you use algebra to describe How can you use algebra to describe the slope of a ramp?the slope of a ramp?
Complete the “Investigating Algebra Activity” on Complete the “Investigating Algebra Activity” on page 234 in your textbook. Complete the page 234 in your textbook. Complete the ‘Drawing Conclusions’ questions #1-6. ‘Drawing Conclusions’ questions #1-6.
What Did We Learn?What Did We Learn?
Slope
Rate of change
m =y2 – y1
x2 – x1
A rate of changerate of change compares a change in
one quantity to change in another quantity.
Homework
Text p. 239, #4-32 evens
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