Equations Of Lines In Slope-Intercept And Standard Form Worksheet Page 2
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9182
(4–26)
Chapter 4 Linear Equations in Two Variables and Their Graphs
Solution
c a l c u l a t o r
a) The y-intercept is (0,
2), and the slope is 3. Use the form y
mx
b with
b
2 and m
3. The equation in slope-intercept form is
c l o s e - u p
y
3x
2.
Since a graphing calculator
b) The y-intercept is (0, 0), and the slope is 1. So the equation is
screen has a finite number of
pixels, a graphing calculator
y
x.
plots only a finite number of
2
ordered pairs that satisfy an
c) The y-intercept is (0, 5), and the slope is
. So the equation is
3
equation. A graph is supposed
2
to be a picture of all of the or-
y
x
5.
I
dered pairs that satisfy an
3
equation. Because a calculator
plots many ordered pairs ac-
The equation of a line may take many different forms. The easiest way to find
curately and quickly, it can be
the slope and y-intercept for a line is to rewrite the equation in slope-intercept
a great help in drawing the
graph of an equation.
form.
E X A M P L E
2
Finding slope and y-intercept
Determine the slope and y-intercept of the line 3x
2y
6.
Solution
Solve for y to get slope-intercept form:
3x
2y
6
2y
3x
6
3
y
x
3
2
I
3
The slope is
, and the y-intercept is (0,
3).
2
Standard Form
The graph of the equation x
3 is a vertical line. Because slope is not defined for
vertical lines, this line does not have an equation in slope-intercept form. Only non-
vertical lines have equations in slope-intercept form. However, there is a form that
includes all lines. It is called standard form.
h e l p f u l
h i n t
In geometry we learn that two
Standard Form
points determine a line. How-
Every line has an equation in the form
ever, if you locate two points
that are close together and
Ax
By
C
draw a line through them,
your line can have a lot of error
where A, B, and C are real numbers with A and B not both zero.
in it at locations far from the
two chosen points. Locating
To write the equation x
3 in this form, let A
1, B
0, and C
3. We get
five points on the graph will
improve your accuracy. If you
1 x
0 y
3,
draw a straight line with two
which is equivalent to
points, they should be chosen
x
3.
as far as possible from each
In Example 2 we converted an equation in standard form to slope-intercept form.
other.
Any linear equation in standard form with B
0 can be written in slope-intercept
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