Find the equation of the line which is parallel to the line 3y-4x=5 and which passes through the midpoint of the line joining (-2,3) and (5,9).
+23252 Every line parallel to 3y - 4x = 5
has the formula: 3y - 4x = k, where different values of k give the different lines.
The midpoint of the line segment whose endpoints are (-2, 3) and (5, 9)
is: ( [-2 +5] / 2 , [3 + 9] / 2 ) = (3/2, 6)
At this point x = 1.5 and y = 6.
Putting these values into: 3y - 4x = k
---> 3(6) - 4(1.5) = k
---> 18 - 6 = k
---> k = 12
So, the final equation is: 3y - 4x = 12
