Question

Which points are on the graph of a linear function? Select all that apply

Answer 1

We will determine the points that belong to a linear function as follows:

*First set: We calculate the slope of the three points:

`m_1=(5-7)/(0-(-1))\Rightarrow m_1=-2`
`m_2=(3-7)/(1-(-1))\Rightarrow m_2=-2`

So, the first set belongs to a linear function.

*second set:

`m_1=(0-1)/(0-(-1))\Rightarrow m_1=-1`
`m_2=(1-1)/(1-(-1))\Rightarrow m_2=0`

So, the second set does not belong to a linear function.

*Third set:

`m_1=(5-5)/(2-0)\Rightarrow m_1=0`
`m_2=(14-5)/(3-0)\Rightarrow m_2=3`

So, the third set does not belong to a linear function.

*Fourth set:

`m_1=(5-(-3))/(2-0)\Rightarrow m_1=4`
`m_2=(13-(-3))/(4-0)\Rightarrow m_2=4`

So, the fourth set belongs to a linear function.