Answer: The required equation of the graphed line is [tex]3x-4y=12.[/tex]
Step-by-step explanation: We are given to find the equation in standard form of the line shown on the graph.
From the graph, we note that
the line passes through the points (4, 0) and (0, -3).
We know that
the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of he graphed line is given by
[tex]m=\dfrac{-3-0}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}.[/tex]
Since (4, 0) is one of the points on the line, so the equation of the graphed line will be
[tex]y-0=m(x-4)\\\\\Rightarrow y=\dfrac{3}{4}(x-4)\\\\\\\Rightarrow 4y=3x-12\\\\\Rightarrow 3x-4y=12.[/tex]
Thus, the required equation of the graphed line is [tex]3x-4y=12.[/tex]
