2.1 & 2.2 Review
Chapter 2 Section 3
Algebra 2 Notes
January 14, 2009
Warm-Ups
2.1 & 2.2 Review!!

Find the slope of the line through following points:

Find the x- and y- intercepts of the line:

Write the same equation in standard form.

Find the slope of the line perpendicular to
2.3 Direct Variation

A linear function with an equation
represents direct variation
◦

is called the constant of variation
In other words, y varies directly with x.
◦ If x is doubled then y is doubled, if x is tripled
then y is tripled, etc.

Some real-world examples?
Identifying Direct Variation

Determine if y varies directly with x
x
2
3
5

y
8
12
20
If it does:
◦ What is the constant of variation, k?
◦ What is the equation of this function?
Identifying Direct Variation

Determine if y varies directly with x
x
1
2
5

y
4
7
16
If it does:
◦ What is the constant of variation, k?
◦ What is the equation of this function?
Identifying Direct Variation

For each function, determine if y varies directly
with x
x
-6
3
12

y
-2
1
4
x
1
2
5
y
4
7
16
x
1
2
5
If it does:
◦ What is the constant of variation, k?
◦ What is the equation of the function?
y
4
7
16
Identifying Direct Variation

Reminder: a function with direct variation is in the form
◦ (Hint: what is the y-intercept??)

Determine if each of these functions represents direct
variation:

If yes:
◦ Find the constant of variation, k
Use a Proportion

In a direct variation function, all the x and y
values are proportional to each other

For example:
x
-6
3
12
y
-2
1
4
Using a Proportions

Suppose y varies directly with x, and
x
= 27 when y = -51. Find x when y = -17
More Proportions

Find the missing value for each direct
variation:
◦ If y = 4 when x = 3, find y when x = 6
◦ If y = 10 when x = -3, find x when y = 2
What Did We Just Cover??

A direct variation function is represented by the
equation

Which means that the constant of variation is
represented by the equation

The x and y values in a direct variation function
are directly proportional
Homework #6
 Pg
74 #1-4, 11-14, 17, 19, 2325, 33, 34

READ EXAMPLE 3 ON PG 73
◦ This will help you with #23 of your HW

2.1 – 2.3 QUIZ ON FRIDAY!!