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Part A: A graph passes through the points (0, 2), (2, 6), and (3, 12). Does this graph represent a linear function or a non-linear function? Explain your answer in words.



Part B: Write one example of a linear function and one example of a non-linear function. (Use x and y as the variables)


Please use full sentences and explain fully.

Verified Answer :

kudzordzifrancis

Part A

The graph passes through \((0,2),(2,6),(3,12)\).


If the graph that passes through these points represents a linear function, then the slope must be the same for any two given points.


Using \((0,2)\) and \((2,6)\).


We obtain the slope to be

\(m=\frac{6-2}{2-0}\)


\(\Rightarrow m=\frac{4}{2}=2\)


Using \((0,2)\) and \((3,12)\).


We obtain the slope to be

\(m=\frac{12-2}{3-0}\)


\(\Rightarrow m=\frac{10}{3}=3\frac{1}{3}\).


Since the slope is not constant(the same) everywhere, the function is non-linear.


Part B

A linear function is of the form

\(y=mx+b\)

where \(m\) is the slope and \(b\) is the y-intercept.

An example is \(y=2x-3\)

A linear function can also be of the form,

\(ax+by=c\) where \(a,b\) and \(c\) are constants.

An example is \(2x+4y=3\)


A non linear function contains at least one of the following,

  • Product of \(x\) and \(y\)
  • Trigonometric function
  • Exponential functions
  • Logarithmic functions
  • A degree which is not equal to \(1\) or \(0\).

An example is \(xy=1\) or \(y=x^2\)or \(y=\sqrt{x}\) etc


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