Answer: The correct option is
(A) \(y=-\dfrac{5}{4}x+3.\)
Step-by-step explanation: We are given to find the slope-intercept equation of the graphed line.
We know that
the slope-intercept equation of a line with slope m and y-intercept c is given by
\(y=mx+c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
From the graph, we note that the slope and y-intercept of the graphed line are
\(m=-\dfrac{5}{4},~~~~~(0,c)=(3,0)~~~\Rightarrow c=3.\)
Substituting the values of m and c in equation (i), we get
\(y=mx+c\\\\\Rightarrow y=-\dfrac{5}{4}+3.\)
Thus, the required slope-intercept equation of the graphed line is \(y=-\dfrac{5}{4}x+3.\)
Option (A) is CORRECT.
