Algebra II
 To
find slope of a line given two
points
 To
find parallel & perpendicular
slope to a line
 Slope
– ratio of vertical change to
horizontal change of a nonvertical line
Line goes through (x1, y1) & (x2, y2)
𝑟𝑖𝑠𝑒 𝑦2 − 𝑦1
𝑆𝑙𝑜𝑝𝑒 = 𝑚 =
=
𝑟𝑢𝑛 𝑥2 − 𝑥1
 Parallel
Lines – have same slope
 Perpendicular
Lines – slopes are
opposite reciprocals
◦ Flip the fraction & change the sign
1. a. Find slope (3, -5)
(x1, y1)
(7, -2)
(x2, y2)
𝑦2 − 𝑦1 −2 − (−5) −2 + 5 3
𝑚=
=
=
=
𝑥2 − 𝑥1
7−3
4
4
b. What is the parallel slope?
3
4
c. What is the perpendicular slope?
4
−
3
Mon
9/21
Learning Objective:
To identify functions
Hw: Pg. 65 # 8 – 11, 14 –
Lesson 16, 17 – 25 odd, 32
2–1
Pg.78 #10 – 16 even. Find
slope, parallel slope, &
perpendicular slope
Algebra II
 To
identify functions
 Relation
– set of pairs of input
and output values
Ways to Represent Relations
 Domain
– set of inputs, “x”
◦ Independent variable
 Range
– set of outputs, “y”
◦ Dependent variable
 Function
– relation in which each
x has exactly one y
 Vertical
Line Test – if a vertical
line passes through more than
one point of the graph, then it is
NOT a function
1. What are the domain and range
of the relation
Domain:
{0, 4, 8, 12, 16|
Range:
{5904, 7696,
8976, 9744, 10000}
2. What are the domain and range
of the relation
{(-3, 14), (0, 7), (2, 0), (9, -18)}
Domain: {-3, 0, 2, 9}
Range: {-18, 0, 7, 14}
3. Is the relation a function?
Is a function! Each x corresponds
with exactly one y.
4. Is the relation a function?
{(4, -1), (8, 6), (6, 6), (4, 1), (1, -1)}
NOT a function! Each x needs to
corresponds with exactly one y.
5. Is the relation a function?
NOT a function! Each x needs to
corresponds with exactly one y.
6. Is the graph a function?
Not a function. Fails the vertical
line test.
7. Is the graph a function?
Is a function. Passes the vertical
line test.
 Function
Notation – f (x)
◦ Represents “y”
◦ “f of x”
◦ “Function f of x”
𝑓 𝑥 = 3𝑥 + 2
𝑦 = 3𝑥 + 2
8. 𝑓 𝑥 = 3𝑥 + 2
Find 𝑓 1
𝑓 1 =3 1 +2
𝑓 1 =3+2
𝑓 1 =5
(1, 5)
9. 𝑓 𝑥 = −4𝑥 + 1
Find 𝑓 −2
𝑓 −2 = −4 −2 + 1
𝑓 −2 = 8 + 1
𝑓 −2 = 9
(-2, 9)
10. Tickets to a concert are $35
each plus a one-time handling fee
of $2.50.
a. Write a function that models the
cost of the concert tickets.
b. Evaluate the function for 6
tickets.
10. a. 𝑓 𝑥 = 35𝑥 + 2.50
b. Find 𝑓 6 for 6 tickets
𝑓 6 = 35 6 + 2.50
𝑓 6 = 210 + 2.50
𝑓 6 = 212.50
$212.50
11. A job offers you $15 per hour
with a bonus of $200.
Another job offers you $20 per
hour with no bonus.
a. Which job would you choose?
b. Write a function that models
each of the job offers.
11. b. Job 1:
Job 2:
𝑓 𝑥 = 15𝑥 + 200
g 𝑥 = 20𝑥
c. How much does each job make
for 30 hours? 40 hours? 50 hours?
30
40
50
Job 1
Job 2
11. b. Job 1:
Job 2:
𝑓 𝑥 = 15𝑥 + 200
g 𝑥 = 20𝑥
c. How much does each job make
for 30 hours? 40 hours? 50 hours?
30
40
50
Job 1
$650
$800
$950
Job 2
$600
$800 $1,000
a. Write a function to model the
cost per month of long distance
cell phone calling plan.
Monthly service fee: $3.12
Rate: $0.18 per minute
b. Evaluate the function for 175
minutes