Answer: The correct equation is (C) [tex]y=\dfrac{1}{2}x+6.[/tex]
Step-by-step explanation: The given equation is
[tex]y-3=\dfrac{1}{2}(x+6)~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
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
[tex]y=mx+c,[/tex]
where 'm' is the slope and 'c' is the y-intercept of the line.
From equation (i), we have
[tex]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.[/tex]
Here, slope, [tex]m=\dfrac{1}{2}[/tex] and y-intercept, [tex]c=6.[/tex]
Therefore, the correct equation is slope-intercept form is
[tex]y=\dfrac{1}{2}x+6.[/tex]
Option (C) is correct.
