Are the functions linear or nonlinear? column a column b 1. 72 = x3 + y 2. y + 1 = 5(x – 9) 3. 7y + 2x = 12 4. 4y = 24 a. linear b. nonlinear

A linear function is given in the form  where  and  are both constant

Function 1:

72 = x³ + y ⇒ rearranging to make 'y' the subject we have
y = -x³ + 72
This function has 'x³' not 'x', so this function is non-linear
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Function 2:

y + 1 = 5(x - 9) ⇒ Multiplying out and simplify like terms
y + 1 = 5x - 45
y = 5x - 45 - 1
y = 5x - 46
This form is exactly the same with y = mx + c so the function is a linear function
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Function 3

7y + 2x = 12
7y = 12 - 2x
7y = -2x + 12
y = ⁻²/₇ x + ¹²/₇

This function does follow the form of linear function so it is a linear function
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Function 4

4y = 24
y = 24/4
y = 6

This function does not have the 'x' term, it means the function is non-linear