The equation of the line passing through the point of intersection of the lines x+2 y+6=0 and 2 x-y=2 and making an intercept 5 on the y -axis is

Step-by-step solution

The given lines are x + 2y + 6 = 0 and 2x - y = 2 , with answer options suggesting the question seeks the angle between them. Rewriting in slope-intercept form, the first line becomes y = - 1 2 x - 3 , with slope m₁ = - 1 2 . The second line is y = 2x - 2 , with slope m₂ = 2 . The product of slopes is m₁ m₂ = - 1 2 2 = -1 , indicating perpendicular lines. The angle between perpendicular lines is 2 radians. Thus, the correct option is D.