The line through (2,y) and (1,-4) is perpendicular to a line with slope (1)/(2) . Find y .

<p> <br />1. The slope of a line perpendicular to a line with slope \( \frac{1}{2} \) is \( -2 \).<br />2. Using the point-slope form of a line and the point (1,-4), we derived the equation \( y = -2x - 2 \).<br />3. Plugging in the x-coordinate of the point (2,y) into the equation, we found that y = -6.<br /></p>