Answer: The correct option is (D) [tex]-7x+7y=-49.[/tex]
Step-by-step explanation: We are given to match the graph with its correct equation.
From the graph, we note that
there is a straight line where the points (7, 0) and (0, -7) lie on it.
So, the slope of the line is given by
[tex]m=\dfrac{-7-0}{0-7}\\\\\\\Rightarrow m=\dfrac{-7}{-7}\\\\\\\Rightarrow m=1.[/tex]
Since the line passes through the point (7, 0), so its equation will be
[tex]y-0=m(x-0)\\\\\Rightarrow y=1(x-7)\\\\\Rightarrow y=x-7\\\\\Rightarrow x-y=7\\\\\Rightarrow -7(x-y)=7\times(-7)\\\\\Rightarrow -7x+7y=-49.[/tex]
Thus, the required equation of the graphed line is [tex]-7x+7y=-49.[/tex]
Option (D) is CORRECT.
