Identify Linear Functions

Linear Function

A linear function’s equation does not have exponents

Exponent

A quantity representing the power to which a given number is to be raised.  Expressed as a raised symbol beside the number or equation (e.g. 3 in 2³)

Question #1

Is y = 6x² + 7 a linear equation?

Step 1

Ask yourself: Are there any exponents?

Yes, y = 6x² + 7 has an exponent: The 2 in x² is an exponent

Answer: y = 6x² + 7 is not a linear equation

Question #2

Is y = 3x + 2 a linear equation?

Step 1

Ask yourself: Are there any exponents?

No, y = 3x + 2 does not have an exponent

Answer: y = 3x + 2 is a linear equation

The form for a Linear Equation

Ax + By = C

Another method, to determine if an equation is linear is to determine whether the equation can be rewritten in linear equation form.

Question #3

Is y = x - 1 a linear equation?

Step 1

Ask yourself: Can y = x – 1 be rewritten in linear equation form?

Step 2

Attempt to put the equation in linear equation form:

Ax + By = C

y = x – 1

To cancel out the ‘-1’ add 1 to both sides:

1 + y = x -1 + 1

1 + y = x

Step 3

Subtract y from both sides to put the equation into linear equation form:

1 + y – y = x – y

1 = x – y

This is linear equation form

Answer: Yes, y = x - 1 is a linear equation

Question #4

Is y = 10x³ + 7 a linear equation?

Step 1

Ask yourself: Can y = 10x³ + 7 be rewritten in linear equation form?

No, linear equation form is: Ax + By = C

No exponents are included in linear equation form.