Perpendicular lines are straight lines that intersect at right angles. The slope of the line with equation y = 1/x + 6 is 1.
If you multiply the slopes of two perpendicular lines, we get -1.
[tex]\frac{1}{2}\times(-2)=-1[/tex]Thus, the line perpendicular to y = 1/2x + 6 has the slope -2
Now use the intercept-slope form to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=-2(x-0) \\ y+2=-2x \\ y+2-2=-2x-2 \\ y=-2x-2 \end{gathered}[/tex]Therefore, the line y = -2x-2 is perpendicular to the line y=1/2x+6 and passes through the y-intercept (0,2)