We have the equations as:
[tex]y - 4 = -8(x - 1)[/tex] as linear,
[tex]y = x^2[/tex] as non-linear,
[tex]y - x^2 = 4.5[/tex] as non-linear,
[tex]3x + 5y = 15[/tex] as linear.
Given equations are:
[tex]y - 4 = -8(x - 1)\\y = x^4\\y - x^2 = 4.5\\3x + 5y = 15[/tex]
A linear function is one which has no more than a unit power of its terms.
A non-linear function is one which has more than 1 power of its in at least one of its terms.
For example, [tex]xy + z = 5[/tex] is not linear since its first term contains two variables [tex]x[/tex] and [tex]y[/tex] thus making total power of the term [tex]xy[/tex] as 2 even when in reality, the power doesn't add up by multiplication due to different bases.
Equation 1:
[tex]y - 4 = -8(x - 1)[/tex]
It is a linear function since all of its terms has got one as its power or no variable.
Equation 2:
[tex]y = x^2[/tex]
It is non linear function since x has 2 as its exponent, which is bigger than one.
Function 3:
[tex]y - x^2 = 4.5[/tex]
It is non linear function since x has 2 as its exponent which is bigger than 1.
Function 4:
[tex]3x + 5y = 15[/tex]
It is linear function since all of its terms has power as 1 or its constant.
Thus, We have the equations as:
[tex]y - 4 = -8(x - 1)[/tex] as linear,
[tex]y = x^2[/tex] as non-linear,
[tex]y - x^2 = 4.5[/tex] as non-linear,
[tex]3x + 5y = 15[/tex] as linear.
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