Given:
The bases of a trapezoid lie on the lines


To find:
The equation that contains the midsegment of the trapezoid.
Solution:
The slope intercept form of a line is

Where, m is slope and b is y-intercept.
On comparing
with slope intercept form, we get

On comparing
with slope intercept form, we get

The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.

The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.




So, the y-intercept of the required line is 1.
Putting m=2 and b=1 in slope intercept form, we get

Therefore, the equation of line that contains the midsegment of the trapezoid is
.