A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #(7 ,8 )#, where is the other end?
The other end is at the point:
Rewrite the given line in slope-intercept form so that we can obtain the slope, m, of the line.
We observe that
The slope, n, of the bisected line is the negative reciprocal of m:
Use this slope and the given point to solve for
The equation of the bisected line is:
Subtract equation  from equation :
The x coordinate of the point two lines intersect is:
The change in x from the point
To go to the other end of the line we must move twice that far in same direction:
The add 7 to find the x coordinate of the other end of the line segment:
To find the y coordinate of the other end of the line segment substitute 14/28 for x in equation :