Let's plot a graph for the equation \(y=-2x+5\text{.}\) We use a table to organize our work:

\(x\) \(y=-2x+5\) Point
\(-2\) \(\phantom{-2(-2)+5=\substitute{9}}\) \(\phantom{(-2,9)}\)
\(-1\) \(\phantom{-2(-1)+5=\substitute{7}}\) \(\phantom{(-1,7)}\)
\(0\) \(\phantom{-2(0)+5=\substitute{5}}\) \(\phantom{(0,5)}\)
\(1\) \(\phantom{-2(1)+5=\substitute{3}}\) \(\phantom{(1,3)}\)
\(2\) \(\phantom{-2(2)+5=\substitute{1}}\) \(\phantom{(2,1)}\)
\(x\) \(y=-2x+5\) Point
\(-2\) \(-2(-2)+5=\substitute{9}\) \((-2,9)\)
\(-1\) \(-2(-1)+5=\substitute{7}\) \((-1,7)\)
\(0\) \(-2(0)+5=\substitute{5}\) \((0,5)\)
\(1\) \(-2(1)+5=\substitute{3}\) \((1,3)\)
\(2\) \(-2(2)+5=\substitute{1}\) \((2,1)\)
(a)Set up the table
(b)Complete the table
Figure4.2.8Making a table for \(y=-2x+5\)

We use points from the table to graph the equation. First, plot each point carefully. Then, connect the points with a smooth curve. Here, the curve is a straight line. Lastly, we can communicate that the graph extends further by sketching arrows on both ends of the line.

a Cartesian grid with points (-2,9),(-1,7),(0,5),(1,3),(2,1)
a Cartesian grid with points (-2,9),(-1,7),(0,5),(1,3),(2,1)
(a)Use points from the table
(b)Connect the points in whatever pattern is apparent
Figure4.2.9Graphing the Equation \(y=-2x+5\)