Section 2.3
Graphing Linear Equations
Linear Equations:
___________________________________
___________________________________
Linear Equations
3 Forms
1. Standard Form ______________
2. Slope-Intercept Form _____________
3. Point-Slope From: ________________
Standard Form
AX + BY = C

X and y are on the same side of the equal sign.

No Fractions or decimals.

X must be positive.

To find the slope from standard form: m = -A/B.

To find x intercept, replace y with zero

To find y intercept, replace x with zero
Slope-intercept form
Y = mx + b

Solved for y

m is the slope

b is the y intercept. (0, b)
Point-Slope Form
y – y1 = m(x – x1)

m = slope

(x1, y1) = point

Use the opposite sign for the points!
Linear Equations always have
infinitely many solutions.

When graphed, the solutions form a
line.

A graph is simply a picture of the
solutions.

Each form of a linear equations has
an easy method to graph.

Graph each.
Standard form. Get the x and y intercept.
1. 2x + 3y = 12
2. 3x – 2y = 4
Graph each.
For Slope-Intercept form, use the y-intercept
and the slope.
3. Y = ¾x – 2
4. y = -2x + 1
Graph each
For Point-Slope form, use the slope and the given
point.
5. Y – 2 = ½ (x + 4)
6. y + 1 = -2/3(x – 4)
Special Lines
Vertical x = c and Horizontal y = c
7. y = -4
8. 3x = -6
You try: Graph using the easiest
method!
1. y = -1/4 x + 1
4. y = -2
2. 3x – 2y = 8
5. Y- 2 = 1/2(x + 3)
3. y = 2x
6. 5y – 2x = 10
Solving Systems of
Equations by Graphing
Section 3.1
System of Equations
• Two or more equations
• Solution: an ordered pair that
makes all equations true.
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How to solve a system by graphing
1. Graph both lines
2. Find the point where they intersect
3. This is the solution because this is
the point that works for both
equations.
Remember the graph is just a picture
of the solutions
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3 Types of Solutions
Exactly one Solution:
Intersecting Lines
Infinitely Many Solutions:
Same Line
No Solution:
Parallel Lines
Different m
Same m and Same b
Same m and Different b
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Find the solution by graphing
1. 2x – 3y = 1
2. 3x – 2y = 6
x+y=3
3x – 2y = 2
Solution:
(2,1)
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Find the solution by graphing
3. 2x – 2y = -8
4. 4x – 3y = -15
2x + 2y = 4
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x + 2y = -1
17
Find the solution by graphing
5. 2x + 4y = 8
x + 2y = 4
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Tell how many solutions each system would have
without graphing.
1. 4x – 3y = 10
8x – 6y = 5
2x – 2y = 15
3. y = 2x + 8
4. 1/2x + 3y = 6
1/3x – 5y = -3
2X – y = -8
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2. 3x + 3y = 10
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Word Problems
Write a system of equations for this
situation. DO NOT SOLVE.
You are buying lotions or soaps for 12 of
your friends. You spent $100. Soaps
cost $5 a piece and lotions are $8.
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Word Problems
Write a system of equations. DO NOT
SOLVE!
Becky has 52 coins in nickels and dimes.
She has a total of $4.65. How many of
each coin does she have?
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Word Problems
Write a system of equations. DO NOT
SOLVE.
There were twice as many students as
adults at the ball game. There were 2500
people at the game.
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