Answer to Question #34527 in Analytic Geometry for daryl

Question

Write the equation of the family of lines. Assign three values to the parameter and graph the lines.

1. The lines are parallel to 4x-7y=3

Answer 1

First put the equation into the form y=mx +b (slope intercept form) as follows:
7y=4x+(-3)
Divide both sides by 7:
y = 4x/7 + (-3/7)

Now m= 4/7 which is your slope. This will be the same for all lines parallel to your equation.

b = -3/7 This is the point where it intercepts the y axis [ie (0, -3/7) This point will vary as the parallel lines may be higher or lower than the original line.

So for the family of parallel lines we need the same slope, but any value for the intercept point, so we can leave that value as 'b'
So the family of parallel lines will be y = 4x/7 + b