SOLUTION
We are told to find the equation of the line passing through the points (2, 5) and parallel to
[tex]y=-\frac{1}{2}x-2[/tex]
Now, equation of line in slope intercept form is given as
[tex]y=mx+b[/tex]
comparing this to
[tex]y=-\frac{1}{2}x-2[/tex]
We can see that m for that equation is
[tex]-\frac{1}{2}[/tex]
m is the slope.
For two parallel lines, m1 = m2. That is their slopes are equal.
So we will use our m as
[tex]m=-\frac{1}{2}[/tex]
For equation of line for point and slope form, we have the formula as
[tex]y-y_1=m(x-x_1)[/tex]
using this, the equation of the line becomes
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \\ y-5_{}=-\frac{1}{2}(x-2) \\ \\ y-5=-\frac{x}{2}+\frac{2}{2} \\ \\ y-5=-\frac{x}{2}+1 \\ \\ y=-\frac{x}{2}+6 \\ \\ y=-\frac{1}{2}x+6 \end{gathered}[/tex]
Therefore, option C is the correct answer
