Answer: The correct equation is (C) \(y=\dfrac{1}{2}x+6.\)
Step-by-step explanation: The given equation is
\(y-3=\dfrac{1}{2}(x+6)~~~~~~~~~~~~~~~~~~~~~(i)\)
We are to identify the equation of the above line in slope-intercept form.
The equation of a straight line in slope-intercept form is given by
\(y=mx+c,\)
where 'm' is the slope and 'c' is the y-intercept of the line.
From equation (i), we have
\(y-3=\dfrac{1}{2}(x+6)\\\\\\\Rightarrow y-3=\dfrac{1}{2}x+3\\\\\\\Rightarrow y=\dfrac{1}{2}x+3+3\\\\\\\Rightarrow y=\dfrac{1}{2}x+6.\)
Here, slope, \(m=\dfrac{1}{2}\) and y-intercept, \(c=6.\)
Therefore, the correct equation is slope-intercept form is
\(y=\dfrac{1}{2}x+6.\)
Option (C) is correct.
