Equations Of Lines In Slope-Intercept And Standard Form Worksheet Page 3
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5
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8
9(4–27)
183
4.3 Equations of Lines in Slope-Intercept and Standard Form
form by solving for y. In the next example we convert an equation in slope-intercept
form to standard form.
E X A M P L E
3
Converting to standard form
2
Write the equation of the line y
x
3 in standard form using only integers.
5
Solution
2
To get standard form, first subtract
x from each side:
5
2
y
x
3
5
2
x
y
3
5
2
5
x
y
5
3
Multiply each side by
5 to eliminate the fraction
5
and get positive 2x.
I
2x
5y
15
The answer 2x
5y
15 in Example 3 is not the only answer using only
integers. Equations such as
2x
5y
15 and 4x
10y
30 are equivalent
equations in standard form. We prefer to write 2x
5y
15 because the great-
est common factor of 2, 5, and 15 is 1 and the coefficient of x is positive.
Using Slope-Intercept Form for Graphing
One way to graph a linear equation is to find several points that satisfy the equation
and then draw a straight line through them. We can also graph a linear equation by
using the y-intercept and the slope.
Strategy for Graphing a Line Using Slope and y-Intercept
1. Write the equation in slope-intercept form if necessary.
2. Plot the y-intercept.
3. Starting from the y-intercept, use the rise and run to locate a second point.
4. Draw a line through the two points.
E X A M P L E
4
Graphing a line using y-intercept and slope
Graph the line 2x
3y
3.
c a l c u l a t o r
Solution
First write the equation in slope-intercept form:
c l o s e - u p
2x
3y
3
To check Example 4, graph
y
3y
2x
3
Subtract 2x from each side.
y
(2 3)x
1 on a graphing
calculator as follows:
2
2
3
y
x
1
y =
x – 1
—
Divide each side by
3.
3
3
3
2
Run = 3
1
2
The slope is
, and the y-intercept is (0,
1). A
Rise = 2
3
– 3
4
x
– 3
– 2
– 1
2
3
4
2
slope of
means a rise of 2 and a run of 3. Start at
3
(0,
1) and go up two units and to the right three
– 2
– 3
units to locate a second point on the line. Now draw
– 3
The calculator graph is consis-
a line through the two points. See Fig. 4.23 for the
tent with the graph in Fig.4.23.
I
graph of 2x
3y
3.
F I G U R E 4 . 2 3
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