Chapter 1: Linear
relations and functions
Section 1-3
Graphing Linear Equations
.
m=
Some Vocabulary
y2 − y1
x2 − x1
If x1 = x2 ( a vertical line), then there is no slope
If y1 = y2 ( a horizontal line), then the slope is 0
• Standard Form Ax +By +C=0
• Slope-intercept form y= mx +b where m is the
slope and b is the y intercept
• X intercept is the point where the line crosses
the x axis
m=
y2 − y1
x2 − x1
y2 − y1
x2 − x1
If x1 = x2 ( a vertical line), then there is no slope
If y1 = y2 ( a horizontal line), then the slope is 0
m=
If x1 = x2 ( a vertical line), then there is no slope
If y1 = y2 ( a horizontal line), then the slope is 0
• Y intercept is the point where the line crosses
the y axis
• Slope is the ratio of the change in the ordinates
of the points (Y) over the change in the
corresponding abscissas (X). Slope is constant
for the line. It is written as
y 2 − y1
m =
x 2 − x1
If x 1 = x 2
( a vertical line),
then there is no slope
If y 1 = y 2 ( a horizontal
then the slope is 0
line),
Graphing a linear
equation
• Set up a table of values
• Choose three values of the
independent variable (x)
• Find the corresponding y that
makes the equation true
• Plot the ordered pairs
• The graph must be a line!
Types of slopes
• Positive slope means the line is
rising
• Negative slope means the line
is descending
• Zero slope means the line is a
horizontal line
• No slope (undefined) means the
line is a vertical line.
Graphing a linear equation
using the slope and y
intercept
• Another way to graph a linear
equation is to write the equation in
slope intercept form ( y= mx +b) .
One of the points is the y intercept b
and is written as (0,b).
• Use the slope to graph the second
point and then draw the line.
Linear Function
A linear function is defined by f (x)= mx+b where m
and b are real numbers.
Values of x for which f (x) = 0 are called zeros of the
function f. The zeros of the function are the x
intercepts.
In the case where m=0 (horizontal line), we have f (x)
= b. This function is called a constant function and
has no zeros UNLESS b=o.
In the case of a vertical line, we do not have a
function.
Example # 1
Graph x + 2y -4=0 using the x and y intercepts.
Find x intercept. Set y=0 then we have
x + 2(0) -4 = 0
x-4 = 0
x=4
Therefore the x intercept is (4,0)
Find the y intercept. Set x = 0, then we have
0 + 2y – 4 = 0
2y = 4
y=2
Therefore the y intercept is (0,2)
Plotting the points and drawing the line, we have the graph below:
Example #2
Find the zero of f (x) = -x -3
Set f (x) = 0 and solve for x
0 = -x-3
-3 = x
-3 is the zero so the coordinates of one point
is (-3,0)
To find another point, set x =0.
We find that when x =0 f (x)= -3. Thus (0, -3)
is the second point.
Plot and draw the line.
HW#3
Section 1-3
PP. 24-25
#12,13,16,17,19,21,25,26,28,29,
33,40,42,43,46