Write an equation for a line perpendicular to \( y=-2 x+5 \) and passing through the point \( (-2,2) \) \( y= \) Question Help: Video Submit Question

To find the equation of a line perpendicular to \( y=-2 x+5 \), we first need to determine the slope of the given line, which is \(-2\). The slope of a line perpendicular to this will be the negative reciprocal, so the slope will be \( \frac{1}{2} \). Using the point-slope form, \( y - y_1 = m(x - x_1) \), we have \( y - 2 = \frac{1}{2}(x + 2) \). Simplifying this yields \( y = \frac{1}{2}x + 3 \). So, the equation of the line is \( y = \frac{1}{2}x + 3 \). This line's slope means for every 2 units you move to the right, you go 1 unit up. Imagine this as a gentle hill - a perfect spot for a leisurely stroll!