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=\frac{5-7}{0-(-1)}\Rightarrow m_1=-2$$m_2=\frac{3-7}{1-(-1)}\Rightarrow m_2=-2$

So, the first set belongs to a linear function.

*second set:

$m_1=\frac{0-1}{0-(-1)}\Rightarrow m_1=-1$$m_2=\frac{1-1}{1-(-1)}\Rightarrow m_2=0$

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

*Third set:

$m_1=\frac{5-5}{2-0}\Rightarrow m_1=0$$m_2=\frac{14-5}{3-0}\Rightarrow m_2=3$

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

*Fourth set:

$m_1=\frac{5-(-3)}{2-0}\Rightarrow m_1=4$$m_2=\frac{13-(-3)}{4-0}\Rightarrow m_2=4$

So, the fourth set belongs to a linear function.