Let's begin by identifying key information given to us:
[tex]y=-x+7[/tex]
In order to graph this equation, we will assume values for the x-variable to obtain the output. This is shown below:
[tex]\begin{gathered} y=-x+7 \\ x=-5 \\ y=-(-5)+7=5+7=12 \\ \Rightarrow(-5,12) \\ \\ x=-1 \\ y=-(-1)+7=1+7=8 \\ \Rightarrow(-1,8) \\ \\ x=2 \\ y=-2+7=5 \\ (2,5) \\ \\ x=4 \\ y=-4+7=3 \\ \Rightarrow(4,3) \\ \\ x=7 \\ y=-7+7=0 \\ \Rightarrow(7,0) \end{gathered}[/tex]
We will proceed to plot this on a graph as shown below:
