Write the equation of the line that is perpendicular

Write an equation in Slope-intercept form for the line that is perpendicular to the line y = 2x - 5 that passes through the given point (4,-2). 

In the line y = 2x - 5,
the slope is 2. 

The perpendicular slope is -1/2 

(4,-2) , m = -1/2   {point and slope}
y - y1 = m(x - x1)   {point-slope form}
y - (-2) = (-1/2)(x - 4)   {substituted point and slope into point-slope form}
y + 2 = (-1/2)x + 2   {used distributive property}
y = (-1/2)x    {subtracted 2 from each side}

- Algebra House