Math Pacing
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1 Graphing Linear Equations ft cm y y / 48 . 30 12 54 . 2
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Graphing Linear Equations. 1. Math Pacing. 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. - PowerPoint PPT Presentation
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1
Graphing Linear Equations
ftcmyy /48.301254.2
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.
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.
Simplify.
Subtract z from each side.
Original equation
Since has 3 different variables, it cannot be written in the form
Answer: This is not a linear equation.
Identify Linear Equations
Rewrite the equation so that both variables are on the same side.
Determine whether is a linear equation.
If so, write the equation in standard form.
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
Answer: The equation is now in standard form where
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.
Determine whether is a linear equation. If so, write the equation in standard form.
Original equation
Factor the GCF.
Divide each side by 3.
Simplify.
Identify Linear Equations
To write the equation with integer coefficients, multiply each term by 4.
Determine whether is a linear equation.
If so, write the equation in standard form.
Original equation
Multiply each side of the equation by 4.
Simplify.
Identify Linear Equations
Answer: The equation can be written asTherefore, it is a linear equation
in standard form where
Determine whether each equation is a linear equation. If so, write the equation in standard form.
a.
b.
c.
d.
Answer: not a linear equation
Answer: linear equation;
Answer: linear equation;
Identify Linear Equations
Answer: linear equation; 4x – y = 5
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
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
Select five values for the domain and make a table.Then graph the ordered pairs.
Multiply each side by 2.
Simplify.
(3, 8)83
(2, 6)62
(0, 2)20
(–1, 0)0–1
(–3, –4)–4–3
(x, y)yx
Graph by Making a Table
Answer:
When you graph the ordered pairs, a pattern begins to form. The domain ofis 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:
.
Graph by Making a Table
