Answer:
y = 1/2 x + 4
Explanation:
The slope intercept form of an equation is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Now in our case the slope m = 1/2; therefore,
[tex]y=\frac{1}{2}x+b[/tex]Now we just need to find the value of b.
Luckily we are told that the line passes through the point (-6, 1), which means that the above equation must satisfy x = -6 given y = 1.
Putting in x = -6 and y = 1 in the above equation gives
[tex]1=\frac{1}{2}(-6)+b[/tex]which simplifies to give
[tex]1=-3+b[/tex]adding 3 to both sides gives
[tex]\begin{gathered} 1+3=-3+b+3 \\ 4=b \end{gathered}[/tex]Hence, the value of b is 4, and therefore, our equation becomes
[tex]\boxed{y=\frac{1}{2}x+4}[/tex]which is our answer!