Answer:
The equation in slope intercept form for a line that will pass through (-6,7) and have a slope of 1/2 is;
[tex]y=\frac{1}{2}x+10[/tex]Explanation:
We want to find the equation of the line in slope-intercept form;
[tex]\begin{gathered} y=mx+b \\ \text{where;} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Given;
[tex]\begin{gathered} m=\frac{1}{2} \\ \text{ point (}x_1,y_1)=(-6,7) \end{gathered}[/tex]Substituting the values into the point slope equation and simplifying;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-7=\frac{1}{2}(x-(-6)) \\ y-7=\frac{1}{2}(x+6) \\ y-7=\frac{1}{2}x+3 \\ y=\frac{1}{2}x+3+7 \\ y=\frac{1}{2}x+10 \end{gathered}[/tex]The equation in slope intercept form for a line that will pass through (-6,7) and have a slope of 1/2 is;
[tex]y=\frac{1}{2}x+10[/tex]