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
Accepted Solution
A:
A linear function is given in the form [tex]y = mx + c[/tex] where [tex]m[/tex] and [tex]c[/tex] 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 ---------------------------------------------------------------------------------------------------------------
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 ----------------------------------------------------------------------------------------------------------------
This function does follow the form of linear function so it is a linear function ------------------------------------------------------------------------------------------------------------
Function 4
4y = 24 y = 24/4 y = 6
This function does not have the 'x' term, it means the function is non-linear