Algebra Concepts
Chapter 3 Notes
Note: We will only cover sections 3-1
and 3-3
Section 3-1 Graphing Linear Equations
Linear Equation –
Standard Form –
Constant -
Section 3-1 Graphing Linear Equations
Linear Equation – an equation that forms a line
when graphed
Standard Form – a linear equation written in the
form Ax + By = C, where A and B cannot both be
zero and C is a constant
Constant – a number (no variable)
Section 3-1
Ex. 1) Determine if the equation is linear. Write
the equation in standard form.
a) y = 4 – 3x
b) 6x – xy = 4
Section 3-1: Finding the x and y
intercepts
Ex) Find the x and y intercepts of the following
equations
1) Plug ________ in for ____ and solve for ____
2) Plug ________ in for ____ and solve for ____
a) 2x + 4y = 16
b) -3x + 12y = 24
Section 3-1: Graphing using the
intercepts, The “Cover-Up” Method
Graph the following equations using the x and y
intercepts.
a) 2x + 4y = 16
b) -3x + 12y = 24
Section 3-1: Graphing using a table
Steps:
1) Make a _______
2) Fill in the ______’s with any values use
choose (Hint: use easy values)
3) Plug each ______ into the equation to find
______
4) Fill in the table with the _______
Section 3-1: Graphing using a table
Ex) Graph the following equations using a table
a) y = 2x – 1
b) y = 1 x + 2
3
Section 3-3: Rate of Change and Slope
Rate of Change –
Ex) Use the table to find the rate of change and
explain its meaning
Number of
Computer
Games
Total Cost
($)
x
y
2
78
4
156
6
234
Section 3-3: Rate of Change and Slope
Rate of Change – If x is the independent variable
and y is the dependent variable, then
Rate of change = Change in y
Change in x
Ex) Use the table to find the rate of change and
explain its meaning
Number of Total Cost
Computer
Games
($)
x
y
2
78
4
156
6
234
Section 3-3: Constant Rate of Change
Ex) Determine whether each function is linear.
a)
b)
x
y
x
y
1
-6
-3
12
4
-8
-1
12
7
-10
1
16
10
-12
3
18
13
-14
5
22
Section 3-3: Slope
Slope –
Positive/Negative Slope –
Steep vs. Flat –
Section 3-3: Slope
Slope – in a non-vertical line, the ratio of the change
in y over the change in x, “rise over run”.
Positive/Negative Slope – if the slope is positive the
line heads to the upper right, if the slope if negative
the line heads toward the lower right
Steep vs. Flat – the bigger the slope, the steeper the
line
Section 3-3: Slope Formula
Slope Formula – The slope of any nonvertical
line through the points(x1, y1 ) and (x2 , y 2 ) can be
found using the formula:
y2 - y1
m=
x2 - x1
Section 3-3: Slope
Ex) Find the slope of a line that passes through
the given points
a) (-2, 0) and (1, 5)
b) (-3, 4) and (2, -3)
c) (-3, -1) and (2, -1)
d) (-4, 2) and (-2, 10)
Section 3-3: Slope
Find the slope of the line that passes through (2, 4) and (-2, -3)
Undefined Slope -
Section 3-3: Slope
Positive Slope
Slope of 0
Negative Slope
Undefined Slope
Section 3-3: Slope
Ex) Find the value of r so that the line through
a) (1, 4) and (-5, r) has a slope of 1/3
b) (-2, 8) and (r, 4) has a slope of ½