If the parallel sides of a trapezoid are contained by the lines y=-1/4x+5 and y=-1/4x-1 , find the equation of the line that contains the midsegment. show equations and all work that leads to your answer.

In this item, we are given the equations of the lines which serves as the bases of the trapezoid. We are asked to determine the equation of the midsegment. 

The midsegment is also parallel to the bases and that the lines can only be parallel if and only if there slopes are equal. The equations given above has the form,
                    y = mx + b 
where m is the slope and b is the y-intercept. Thus, the slope is equal to -1/4. Also, the y-intercept of the midsegment will be the average of those from the bases. 
                     y-intercept = (5 - 1) / 2 = 2

Hence, the equation of the midsegment is,
              y = -1/4x + 2