A table with a constant change represents a linear function.
[tex]\mathbf{(a)\ 3x + 5y = 4}[/tex]
Make y the subject
[tex]\mathbf{y = \frac{4 - 3x}5}[/tex]
When x = 0, 1 and 2, we have:
[tex]\mathbf{y = \frac{4 - 3(0)}5 = \frac{4}{5}}[/tex]
[tex]\mathbf{y = \frac{4 - 3(1)}5 = \frac{1}{5}}[/tex]
[tex]\mathbf{y = \frac{4 - 3(2)}5 = \frac{-2}{5}}[/tex]
[tex]\mathbf{3x + 5y = 4}[/tex] represents a linear function.
So, it has a constant change, and the change is -3/5
[tex]\mathbf{(b)\ 4x^2 + y = 4}[/tex]
Make y the subject
[tex]\mathbf{y = 4 - 4x^2}[/tex]
When x = 1 and 2, we have:
[tex]\mathbf{y = 4 - 4(1)^2 = 0}[/tex]
[tex]\mathbf{y = 4 - 4(2)^2 = -12}[/tex]
[tex]\mathbf{y = 4 - 4x^2}[/tex] is not a linear function.
So, it does not have a constant change
[tex]\mathbf{(c)\ 6x + 1 = y}[/tex]
Make y the subject
[tex]\mathbf{y = 6x + 1}[/tex]
When x = -1, 0, 1 and 2, we have:
[tex]\mathbf{y = 6(-1) + 1 = -5}[/tex]
[tex]\mathbf{y = 6(0) + 1 = 1}[/tex]
[tex]\mathbf{y = 6(1) + 1 = 7}[/tex]
[tex]\mathbf{y = 6(2) + 1 = 13}[/tex]
[tex]\mathbf{y = 6x + 1}[/tex] represents a linear function.
So, it has a constant change, and the change is 6
See attachment for the complete table
Read more about linear functions at:
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