Page 34 - Math Course 1 (Book 2)

Linear Equations

Mo. 8

Lesson 1
Let’s Begin

KEY CONCEPTS:
1. Identify linear equations. Identify Linear Equations
2. Graph linear equations.
3. Identify intercepts and zeros.
Examples

Determine whether 5x + 3y = z + 2 is a linear
equation. If so, write the equation in standard
MO. 8 - L1a form.

Identify Linear Equations First rewrite the equation so that the variables are
on the same side of the equation.

5x + 3y = z + 2 Original equation
Vocabulary A-Z 5x + 3y – z = z + 2 – z Subtract z from each
side.
Let us learn some vocabulary
5x + 3y – z = 2 Simplify

Since 5x + 3y – z has three different variables, it
cannot be written in the form Ax + By = C.
linear equation
is the equation of a line.
Answer This is not a linear equation.
Linear Equation
3
Ax+By = C Determine whether is a linear equation.
x = y + 8
4
A, B, and C, are If so, write the equation in standard form.
numbers
Rewrite the equation so that both variables are on
the same side of the equation.

standard form 3 x = y + 8 Original equation
4
Linear equations can often be written in the form 3 x – y = y + 8 –y Subtract y from each
Ax + By = C. This is called the standard form of a 4 side.
linear equation. 3
Ax + By = C 4 x – y = 8 Simplify

Key Concept To write the equation with integer coef cients,
multiply each term by 4.
3 x – y = 8 Original equation
4
Standard Form of a Linear Equation 3 Multiply each side of
4 x –4(y) = 8(4)
4 the equation by 4.
The standard form of a linear equation is 3x – 4y = 32
Ax + By = C, Simplify
The equation is now in standard form where A = 3,
where A ≥ 0, A and B are not both zero, and A, B, B = –4, and C = 32.
and C are integers with a greatest common factor
of 1.
Answer This is a linear equation.

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