You do need to solve if you want an exact answer. After drawing a line through the left and right points, find the equation of that line (this is not the final line). You will already know the x value of the middle point, so that needs to be substituted into the equation so a y value can be found along the line that you have drawn.

Once this y value is known, you can multiply the difference between this point on the original line and the middle point's y value by 1/3. The line can be moved 1/3 of the way up using the same gradient. You can then solve for the y-intercept.