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Linear Relationships, SM-Bank 044

  1. Complete the table of values using the graph of the straight line below.  (2 marks)
    \begin{array} {|l|c|c|c|}
    \hline
    \rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 & -1  &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \  \\
    \hline
    \rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} &  &   &   &  & \\
    \hline
    \end{array}
     
  2. Using either the table or the graph, state the rule connecting \(\large x\) and \(\large y\).  (1 mark)

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a.

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 &  -1  &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 3 & 2  &  1 & 0 & -1 \\
\hline
\end{array}

 b.    \(y=-x+1\)

Show Worked Solution

a.    \(\text{Table of values}\)

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 &  -1  &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 3 & 2  &  1 & 0 & -1 \\
\hline
\end{array}

 b.    \(\text{The }y\ \text{values are decreasing by } 1\ \text{and when }x=0,\ \ y=1\)

\(\therefore\ \text{Rule:  }y=-x+1\)