1. 2.1 Review
When variables change together, their interaction is called a ___________.
When one variable determines the exact value of a second variable, their relation is called a ____________.
The parts of a function are called _________ and output.
The input is the ____________, non-repeating quantity.
The output is the dependent ___________.
For each input, there is a ________ output.
Function Notation:
Is the relation between cars and tires a function? What about houses and tenants?

2. Function or not? Why?
Remember, when a single input can produce multiple outputs, the relation is not a function.
X values cannot be repeated in a function.

3. Which of the following is a set of ordered pairs representing a function?
B) {(0, 0), (1, 1), (1, -1), (2, 2), (2, -2)}
C) (4, 2), (5, 1), (6, 0), (7, -1), (8, -2)
D) {(-2, 2), (-1, 1), (0, 0), (1, 1), (2, 2)}
ANSWER D

4. All horizontal lines represent a function. Why
All horizontal lines represent a function. Why? What about vertical lines?
ANSWER
A line on the coordinate plane is horizontal when every x-coordinate has the same y-coordinate.
No x-coordinates have more than one y-coordinate, and each input always produces the same output.
Vertical lines do not represent a function because one x value is paired with many y values.

5. 2.1 Review
Graph the equation y = 3x - 2 x -2 -1 1 2 y -8 -5 4

6. 2.1 Review
Graph the equation y = -1/2x +1 x -2 -1 1 2 y
1.5
0.5

7. 2.1 Review g(-2) = -4 – 2(-2) = -4 – -4 = -4 + 4 = 0
Tell whether the function is linear, then evaluate it when x = -2
g(x) = -4 – 2x
Yes, the function is linear. Why?
g(-2) = -4 – 2(-2)
= -4 – -4 =
= 0

9. EXAMPLE 2
Standardized Test Practice
SOLUTION
Let (x1, y1) = (–1, 3) and (x2, y2) = (2, –1).
m =
y2 – y1
x2 – x1 =
– 1 – 3
2 – (–1) = 4 3
ANSWER
The correct answer is A.

10. GUIDED PRACTICE
for Examples 1 and 2
(7, 3), (– 1, 7)
SOLUTION
Let (x1, y1) = (7, 3) and (x2, y2) = (– 1, 7).
m =
y2 – y1
x2 – x1 =
7 – 3
– 1 – 7 = 1 2 –
ANSWER 1 2 –

11. Classify lines using slope
EXAMPLE 3
Classify lines using slope
Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a.
(– 5, 1), (3, 1) b.
(– 6, 0), (2, –4) c.
(–1, 3), (5, 8) d.
(4, 6), (4, –1)
SOLUTION
1 – 1
3– (–5) =
m = a. 8
= 0
Because m = 0, the line is
horizontal.
– 4 – 0
2– (–6) =
m = b.
– 4 8 = 1 2 –
Because m < 0, the line falls.

12. Classify lines using slope
EXAMPLE 3
Classify lines using slope
Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a.
(– 5, 1), (3, 1) b.
(– 6, 0), (2, –4) c.
(–1, 3), (5, 8) d.
(4, 6), (4, –1)
SOLUTION
1 – 1
3– (–5) =
m = a. 8
= 0
Because m = 0, the line is
horizontal.
– 4 – 0
2– (–6) =
m = b.
– 4 8 = 1 2 –
Because m < 0, the line falls.

13. a. b. EXAMPLE 4 Classify parallel and perpendicular lines
Tell whether the lines are parallel, perpendicular, or
neither.
Line 1: through (– 2, 2) and (0, – 1) a.
Line 2: through (– 4, – 1) and (2, 3)
Line 1: through (1, 2) and (4, – 3) b.
Line 2: through (– 4, 3) and (– 1, – 2)
SOLUTION
Find the slopes of the two lines. a.
m1 =
–1 – 2
0 – (– 2) =
– 3 2 3 2 –

14. EXAMPLE 4
Classify parallel and perpendicular lines
m2 =
3 – (– 1)
2 – (– 4) = 4 6 2 3
ANSWER
Because m1m2 = – 2 3
= – 1, m1 and m2
are negative reciprocals of each other. So, the lines are perpendicular.

15. EXAMPLE 4
Classify parallel and perpendicular lines
Find the slopes of the two lines. b.
m1 =
–3 – 2
4 – 1 =
– 5 3 = 5 3 –
m2 =
– 2 – 3
– 1 – (– 4) =
– 5 3 = 5 3 –
ANSWER
Because m1 = m2 (and the lines are different), you can conclude that the lines are parallel.