Answer: The slope-intercept form of the equation of the line is
\(y=\dfrac{4}{3}x-4.\)
Step-by-step explanation: We are to find the slope-intercept form of the equation of the line shown in the graph.
The points (3, 0) and (0, -4) are two points on the line.
So, the slope of the line will be
\(m=\dfrac{-4-0}{0-3}=\dfrac{4}{3}.\)
Since the line passes through the point (3, 0), so the equation of the line will be
\(y-0=\dfrac{4}{3}(x-3)\\\\\\\Rightarrow y=\dfrac{4}{3}(x-3)\\\\\\\Rightarrow 3y=4x-12\\\\\\\Rightarrow y=\dfrac{4}{3}x-4.\)
Therefore, the slope-intercept form of the equation of the line is
\(y=\dfrac{4}{3}x-4.\)
Thus, option (D) is correct.
