Final answer:
The equation of the line perpendicular to line QR, in slope-intercept form and containing the point (5, 6), is y = 2x - 4.
Step-by-step explanation:
To find the equation of a line that is perpendicular to line QR, we need to determine the slope of line QR and then find the negative reciprocal of that slope. The equation of line QR is given as x + 2y = 2. To rewrite this equation in slope-intercept form, we isolate y and write it as y = -1/2x + 1. The slope of line QR is therefore -1/2. The negative reciprocal of -1/2 is 2, so the equation of the line perpendicular to line QR is y = 2x + b. To find the value of b, we substitute the coordinates of the given point (5, 6) into the equation and solve for b. Plugging in the values, we get 6 = 2(5) + b. Solving for b, we find b = -4. Therefore, the equation of the line perpendicular to line QR that contains the point (5, 6) is y = 2x - 4, which corresponds to option B.