Question

For each equation, determine whether it is linear.

(a) y=4
Equation
(b) y=-4x²+3
(c) y=7x+2
(d) y=-x
Is the equation linear?
Yes
No

Answer 1

(a) yes

(b) no

(c) yes

(d) yes

Explanation:

You want to know which of these equations is linear.

• y = 4
• y = -4x² +3
• y = 7x +2
• y = -x

Linear equation

For the purpose here, we will define a linear equation as one that graphs as a straight line. (Other definitions may give different answers.)

In general, a linear equation will have a highest degree of 1. (It may be 0.)

The equation of choice (b) has degree 2, so is not a linear equation.

Graph

The attached graph shows the only equation that is not linear is choice (b).

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Additional comment

In some branches of mathematics, an equation of the form y = mx+b is not a linear equation. In basic algebra, that is the model of a linear equation, for any values of m and b.