Download Graphing Linear Equations

Graphing
Linear
Equations
By Using Intercepts
Before we begin graphing, let’s review writing
equations in standard form, ax + by = c.
Example 1: Rewrite the equations in standard
form.
a) 3x + 4 = 2y
b)
5x – 2y = 15
3x – 2y = – 4
c) 5y – 4x = 20
–4x + 5y = 20
5(x – 3) = 2y
d)
½x + ¾y = 1
2x + 3y = 4
Linear Equation
An equation for
which the graph is
a line
Solution
Any ordered pair of
numbers that
makes a linear
equation true.
5x + 2y = 10
.( 0 , 5 )
.(2 , 0)
X-intercept
Where the line
crosses the
x-axis
X-intercept
The x-intercept has
a y coordinate of
ZERO
X-intercept
To find the xintercept, plug in
ZERO for y and
solve
Y-intercept
Where the line
crosses the
y-axis
Y-intercept
The y-intercept has
an x-coordinate of
ZERO
Y-intercept
To find the yintercept, plug in
ZERO for x and
solve
1. Find your x-intercept:
Let y = 0
-2x + 3y = 12
-2x + 3(0) = 12
-2x = 12
-2 -2
x = -6; (-6, 0)
2. Find your y-intercept:
Let x = 0
-2(0) + 3y = 12
3y = 12
3
3
y = 4; (0, 4)
Graph
-2x + 3y = 12
3. Graph both points
and draw a line through
them.
4x + y = 8
1. Find your x-intercept:
Let y = 0
4x + 0 = 8
4x = 8
4
4
x = 2; (2, 0)
2. Find your y-intercept:
Let x = 0
0+y=8
y=8
y = 8; (0, 8)
Graph
4x – 8 = –y
3. Graph both
points and
draw a line
through them.
-2x + 3y = 15
1. Find your x-intercept:
Let y = 0
-2x + 3(0) = 15
-2x = 15
-2 -2
x = -15/2; (-15/2, 0)
2. Find your y-intercept:
Let x = 0
-2(0) + 3y = 15
3y = 15
3
3
y = 5; (0, 5)
Graph
3y – 15 = 2x
3. Graph both points
and draw a line through
them.
2x + 5y = 10
1.Find your x-intercept:
Hide the variable y
Graph
2x – 10 = – 5y
2x = 10
2
2
x = 5; (5, 0)
2. Find your y-intercept:
Hide the variable x
5y = 10
5
5
y=2
y = 2; (0, 2)
3. Graph both
points and
draw a line
through them.
–2x – 5y = 20
1.Find your x-intercept:
Hide the variable y
Graph
– 5y = 2x + 20
-2x = 20
-2 -2
x = -10; (-10, 0)
2. Find your y-intercept:
Hide the variable x
-5y = 20
-5 -5
y = -4
y = -4; (0, -4)
3. Graph both
points and
draw a line
through them.
Determine the x- and y-int. of the ff.
x-int. y-int.
1.3x + y = 3
2.2x + 5y = 10
3.4x – 6y = 12
4.6x = 2y – 4
5.x = 2y + 7
1
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5
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3
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-2/3
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7
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3
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2
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-2
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2
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-7/2
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Seatwork:
A. Determine the x- and y-int. of the ff.
x-int.
1. 2x + y = 4
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2. x – y = 5
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3. y = –x + 3
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4. y = 2x + 3
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5. x = y – 6
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B. Graph nos. 4 and 5
y-int.
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