(Refer to Example 1.) Is the equation linear? If it is linear, give values for a and b tha...

(Refer to Example 1.) Is the equation linear? If it is linear, give values for a and b that result when the equation is written in the form ax + b = 0.

2(x − 3) = 0

EXAMPLE 1 Determining whether an equation is linear

Determine whether the equation is linear. If the equation is linear, give values for a and b that result when the equation is written in the form ax + b = 0.

(a) 4x + 5 = 0

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(b)

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(c) 4x2 + 6 = 0

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(d)

Solution

(a) The equation is linear because it is in the form ax + b = 0 with a = 4 and b = 5.

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(b) The equation can be rewritten as follows.

 

The given equation is linear because it can be written in the form ax + b = 0 with and b = 5.

NOTE: If 5 had been subtracted from each side, the result would be , which is an equivalent linear equation with and b = −5.

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(c) The equation is not linear because it cannot be written in the form ax + b = 0. The variable has exponent 2.

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(d) The equation is not linear because it cannot be written in the form ax + b = 0. The variable appears in the denominator of a fraction.