Graphing Linear Equations
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Graphing Linear Equations
A linear equation can be written in the
standard form of a linear equation:
Ax + By = C,
where A ≥ 0,
A and B are not both zero, and
A, B and C are integers whose greatest
common factor is 1.
Identify Linear Equations
Determine whether
is a linear
equation. If so, write the equation in standard form.
First rewrite the equation so that the variables are
on the same side of the equation.
Original equation
Subtract z from each side.
Simplify.
Since
has 3 different variables, it cannot be
written in the form
Answer: This is not a linear equation.
Identify Linear Equations
Determine whether
is a linear equation.
If so, write the equation in standard form.
Rewrite the equation so that both variables are on
the same side.
Original equation
Subtract y from each side.
Simplify.
Identify Linear Equations
To write the equation with integer coefficients, multiply
each term by 4.
Original equation
Multiply each side of the
equation by 4.
Simplify.
The equation is now in standard form where
Answer: This is a linear equation.
Identify Linear Equations
Determine whether
is a linear equation.
If so, write the equation in standard form.
Since the GCF of 3, 6, and 27 is not 1, the equation is not
written in standard form. Divide each side by the GCF.
Original equation
Factor the GCF.
Divide each side by 3.
Simplify.
Answer: The equation is now in standard form
where
Identify Linear Equations
Determine whether
is a linear equation.
If so, write the equation in standard form.
To write the equation with integer coefficients,
multiply each term by 4.
Original equation
Multiply each side of the
equation by 4.
Simplify.
Answer: The equation
can be written as
Therefore, it is a linear equation
in standard form where
Identify Linear Equations
Determine whether each equation is a linear equation.
If so, write the equation in standard form.
a.
Answer: linear equation;
4x – y = 5
b.
Answer: not a linear equation
c.
Answer: linear equation;
d.
Answer: linear equation;
Graphing Linear Equations
The graph of a linear equation is a line.
The line represents all the solutions of the
linear equation.
Also, every ordered pair on this line
satisfies the equation.
Graph by Making a Table
Graph
In order to find values for y more easily, solve the
equation for y.
Original equation
Add x to each side.
Simplify.
Graph by Making a Table
Multiply each side by 2.
Simplify.
Select five values for the domain and make a table.
Then graph the ordered pairs.
x
–3
–1
0
2
3
y
–4
0
2
6
8
(x, y)
(–3, –4)
(–1, 0)
(0, 2)
(2, 6)
(3, 8)
Graph by Making a Table
Answer:
When you graph the ordered
pairs, a pattern begins to form.
The domain of
is the set of all real numbers,
so there are an infinite number
of solutions of the equation.
Draw a line through the points.
This line represents all the
solutions of
.
Graph by Making a Table
.
Answer: