ALGEBRA 2 LECTURE 1 – 1: Data and Linear Representations
Reading Assignment: Chapter 1, Pages 2 – 28
LINEAR EQUATIONS
Linear Relationship
 A constant difference in consecutive x-values results in a constant difference in y-values.
 The relationship between x and y can be written as y = mx + b, where m and b are real
numbers.
 The equation y = mx + b is called a linear equation.
 The graph of a linear equation is a straight line.
 Page 8 #4
A.
Weekly Sales,
Weekly income, y
x
100
50 (0.15)(100) = 65
200
300
400
x
B.
C. Linear Equation:
D. Find the weekly income, y, for weekly sales of $1200.
ALGEBRA 2 LECTURE 1 – 1: Data and Linear Representations
TRY THIS Page: 5
A water tank already contains 55 gallons of water when Darius begins to fill it. Water flows into
the tank at a rate of 9 gallons per minute.
A. Make a table for the volume of water in the tank after 1, 2, 3, and 4 minutes.
Time Elapsed (Minutes) Volume of water (Gallons)
1 Minute
2 Minutes
3 Minutes
4 Minutes
B. Graph the points represented by your table and connect them.
C. Linear Equation:
D. Volume after 20 minutes:
TRY THIS Page 7
Does the table below represent a linear relationship between x and y? Explain.
x
y
–2
1
2
2
6
4
10
8
14
16
18
32
ALGEBRA 2 LECTURE 1 – 1: Data and Linear Representations
SLOPES and INTERCEPTS
Slope of a Line
 If points (x1, y1) and (x2, y2) lie on a line, then the slope, m, of the line is given by:

The slope of a line tells you about the steepness and direction of the line.
Intercepts
 The y-intercept is the y-coordinate of the point where the graph of a linear equation
crosses the y-axis.
 The y-intercept is the y-coordinate of the point where x = 0.
 The x-intercept is the x-coordinate of the point where the graph crosses the x-axis.
 The x-intercept is the x-coordinate of the point where y = 0.
Slope-Intercept Form
 y = mx + b, where m is the slope and b is the y-intercept
Standard Form
 Ax + By = C, where A, B, and C are real numbers, A is positive, and A and B are not
both 0.
Horizontal and Vertical Lines
 A horizontal line is a line that has a slope of 0.
 A vertical line is a line that has an undefined slope.
PAGE 17 # 5 – 8
5. Find the slope of the line containing the points (– 2, 4) and (8, – 3 )
6. Use the slope and y-intercept to graph ½ x +y = – 4
ALGEBRA 2 LECTURE 1 – 1: Data and Linear Representations
7. Write the equation in slope-intercept form for the line graphed on page 17.
8. Use intercepts to graph – 2x – 4y = 8
TRY THIS Page 13
Find the slope of the line containing the points (– 5, 3) and (3, – 4).
TRY THIS Page 15 (Ex. 2)
Use the Slope and y-intercept to graph the equation 2x + y = 3.
ALGEBRA 2 LECTURE 1 – 1: Data and Linear Representations
TRY THIS Page 15 (Ex. 3)
Write the equation, in slope-intercept form, for the line that passes through (1, 4) and has a yintercept of 3.
TRY THIS Page 16
Use intercepts to graph the equation 5x + 3y = 15.
LINEAR EQUATIONS IN TWO VARIABLES
Point-Slope Form
 y – y1 = m ( x – x1 ), where m is the slope and (x1, y1) is a point on the line.
Parallel Lines
 If two lines have the same slope, they are parallel.
 If two lines are parallel, they have the same slope.
 All vertical lines have an undefined slope and are parallel to one another.
 All horizontal lines have a slope of 0 and are parallel to one another.
Perpendicular Lines
 If a non-vertical line is perpendicular to another line, the slopes of the lines are negative
reciprocals of one another.
 All vertical lines are perpendicular to all horizontal lines.
 All horizontal lines are perpendicular to all vertical lines.
TRY THIS Page 24
Write an equation in slope-intercept form for the line that contains the point (– 3, – 4) and is
parallel to the graph of y = – 4x – 2.
Hw. Pages 8-9 #15,17,19,29,31,35,39,49 ;
p.17-18 # 15,17,19,25,37,39,41,43, 65;
p 26-27 # 15,17,25, 29,35,43,63