linear equations form a straight line when graphed.

standard form: Ax + By = C

• A, B, and C are written as integers.
• A should be positive.
• C is called the constant. it is not multiplied by anything.

example 1: determine if a linear equation.
try and put it in standard form.

5x + 3 = xy + 2

first, cancel out the three:

5x + (3 - 3) = xy + (2 - 3)

and get:

5x = xy + (-1), or 5x = xy - 1

cancel out xy:

5x - xy = (xy - xy) - 1

and get:

5x - xy = -1

thus, the equation is not a linear equation, because B is a variable, and A, B, and C must be integers.

example 2: determine if a linear equation.
try and put it in standard form.

¾x = y + 8

first, get rid of the fraction by multiplying by the LCD:

4(¾x) = 4(y + 8)

and get:

3x = 4y + 32

cancel out 4y:

3x - 4y = (4y - 4y) + 32

and get:

3x - 4y = 31

thus, the equation is linear.