Transcript Ch 4-5 Graphing Linear Equations
Graphing Linear Equations 1
y
2 .
54
y
30 .
48
cm
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ft
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 written in the form has 3 different variables, it cannot be
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; 4
x
–
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
equation for
y
.
more easily, solve the 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)
Answer:
Graph by Making a Table 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 .
Answer:
Graph by Making a Table
.