Equations Of Lines In Slope-Intercept And Standard Form Worksheet
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4.3 Equations of Lines in Slope-Intercept and Standard Form
E Q U A T I O N S O F L I N E S I N S L O P E -
4.3
I N T E R C E P T A N D S T A N D A R D F O R M
In Section 4.1 you learned that the graph of all solutions to a linear equation in two
I n t h i s
variables is a straight line. In this section we start with a line or a description of a
s e c t i o n
line and write an equation for the line. The equation of a line in any form is called a
linear equation in two variables.
Slope-Intercept Form
G
Slope-Intercept Form
Standard Form
G
Using Slope-Intercept Form
2
G
Consider the line through (0, 1) with slope
shown in Fig. 4.22. If we use the points
3
for Graphing
(x, y) and (0, 1) in the slope formula, we get an equation that is satisfied by every
Writing the Equation for a
G
point on the line:
Line
y
y
Applications
G
2
1
m
Slope formula
x
x
2
1
y
1
2
Let (x
, y
)
(0, 1) and (x
, y
)
(x, y).
1
1
2
2
x
0
3
y
y
1
2
5
(x, y)
x
3
4
3
Now solve the equation for y:
y – 1
2
y
1
2
x
x
Multiply each side by x.
(0, 1)
x – 0
x
3
x
– 3
– 2
– 1
1
2 3 4 5
2
– 1
y
1
x
3
F I G U R E 4 . 2 2
2
y
x
1
Add 1 to each side.
3
Because (0, 1) is on the y-axis, it is called the y-intercept of the line. Note how
s t u d y t i p
2
2
the slope
and the y-coordinate of the y-intercept (0, 1) appear in y
x
1.
For
3
3
Keep reviewing. After you
this reason it is called the slope-intercept form of the equation of the line.
have done your current as-
signment, go back a section or
Slope-Intercept Form
two and try a few problems.
You will be amazed at how
The equation of the line with y-intercept (0, b) and slope m is
much your knowledge will im-
y
mx
b.
prove with a regular review.
E X A M P L E
1
Using slope-intercept form
Write the equation of each line in slope-intercept form.
a)
b)
c)
y
y
y
(0, 5)
3
4
2
3
4
(3, 3)
1
2
3
(1, 1)
(2, 2)
2
x
– 2
– 1
(0, 0)
1
2
3
– 1
1
x
– 2
– 1
1
2
3
– 2
– 1
(0, – 2)
x
– 1
1
2 3 4
– 2
– 1
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