Transcript Section 3.1, S–7 Slope from two points

Section 3.1, S–7
Slope from two points: Take west to be the positive direction. The height
of a sloped roof above the place where I stand is 12 feet (see figure). If I
move 3 feet west, the height is 10 feet. What is the slope?
12 ft
10 ft
3 ft
West
Section 3.1, S–7
Slope from two points: Take west to be the positive direction. The height
of a sloped roof above the place where I stand is 12 feet (see figure). If I
move 3 feet west, the height is 10 feet. What is the slope?
S-8 If I move 5 additional feet west,
what is the height of the roof
above the place where I stand?
12 ft
10 ft
3 ft
West
5 ft
Section 3.1, exercise 7
A ramp to a building: The base of a ramp sits on the ground (see figure).
Its slope is 0.4, and it extends to the top of the front steps of a building
15 horizontal feet away.
a. How high is the ramp 1 horizontal foot toward the building from
the base of the ramp?
b. How high is the top of the steps relative to the ground.
15 ft
1 ft
Section 3.1, exercise 13
Looking over a wall: Twenty horizontal feet north of a 50-foot building is
a 35-foot wall (see figure). A man 6 feet tall wishes to view the top of the
building from the north side of the wall. How far north must he stand in order
to view the top of the building?
35 ft
50 ft
20 ft
North
Section 3.1, exercise 13
Looking over a wall: Twenty horizontal feet north of a 50-foot building is
a 35-foot wall (see figure). A man 6 feet tall wishes to view the top of the
building from the north side of the wall. How far north must he stand in order
to view the top of the building?
35 ft
50 ft
6 ft
?
20 ft
North
Answers to even-numbered HW problems
Section 3.1
S-2 The slope is 5.
S-8 The height is 6 32 feet.
y
Ex 2 The horizontal intercept is -3.

x
y
Ex 4 The vertical intercept is -18.

x
LINEAR
FUNCTIONS
A linear function is a function whose graph is a line.
A linear function can have several different forms algebraically.
Slope-intercept form
y = mx + b
1
Example y = x – 2
2
1
m= ,
2

b = –2
●

slope
y-intercept
x
Where have we already encountered
linear functions in this course?
Plan 1. $15.00 per month plus 10 cents a minute.
Plan 2. $30.00 per month plus 6 cents per minute.
Using C for cost and N for number of minutes, use a formula to express the cost
of plan 1 as a function of the number of minutes used per month.
C = .10N + 15
Using C for cost and N for number of minutes, use a formula to express the cost
of plan 2 as a function of the number of minutes used per month.
C = .06N + 30
The graph of a linear function is a line.
A linear function can have several different forms algebraically.
Slope-intercept form
y = mx + b
C = .10N + 15
1
Example y = x – 2
2
1
m= ,
2

b = –2
x
●

slope
y-intercept
Find the slope and y-intercept of each linear function below:
y = 3x + 8
y = –x +

1
2
Slope = 3, y-intercept = 8
1
Slope = –1, y-intercept =
2

y




x
Find the slope and y-intercept of each linear function below:
y = 3x + 8
1
2
1
Slope = –1, y-intercept =
2
x
y= 3–7

1
Slope = , y-intercept = –7
3

y = –x +
y = 5x

Slope = 3, y-intercept = 8
Slope = 5, y-intercept = 0

y



x

Practice writing equations for linear functions
Example 1:
Write the equation of a line whose slope is 2 and
whose y-intercept is –7.
Example 2:
Write the equation of a line whose slope is 2 and
that passes through the point (3, 10).

10
9

8
7
6
5
4
3
2
Slope-intercept form
y = mx + b
1
1
2
3
4
5
6
7
8
9
Practice writing equations for linear functions
Example 1:
Write the equation of a line whose slope is 2 and
whose y-intercept is –7.
Example 2:
Write the equation of a line whose slope is 2 and
that passes through the point (3, 10).
Example 3:
Write the equation of a line that passes through the
points (-5, 0) and (1, 4).
Example 4:
If f is a linear function such that f(7) = 24 and
f(4) = 6, find the equation for f.
Slope-intercept form
y = mx + b
Graph each linear function below
2
y= x+4
5
y
8

7
6
y – 1 = 2(x + 3)
5

4
3
2
1
1
2
3
4
5
6
7
8
9
x
An elementary school is taking a busload of children to a science fair. It
costs $130.00 to charter the bus, and the school pays each student’s $2.50
admission fee.
1.
Explain why the total cost of the science fair trip a linear function of the
number of students who go to the science fair.
2.
Use a formula to express the total cost C, in dollars, of the science fair
trip as a function of the number n of children who make the trip.
3.
Identify the slope of C, and explain in practical terms what they mean.
4.
If the linear function is graphed, where would the line cross the y-axis?
How can this value be interpreted in the science fair context?
The y-intercept is also called the
initial value of the function.
Homework:
Read Section 3.2 (through middle of page 234)
Page 239 # S-1, S-2, S-3, S-7, S-8, S-9, S-19, S-21
Pages 240 – 242 # 1, 8, 11
and revisit the problems from Section 3.1