Question

write an equation for the locus of points equidistant from the lines whose equations are y=3x-4 and y=3x+10

Answer 1

These are parallel lines so it would be a line parallel to these lines but half way between them.

Answer 2

y=3x+10 -(i)
y=3x-4 -(ii)

As @Mertsj has mentioned, you have the slope of the equation (since it's the same slope as the other 2 lines)
Since it's the midway of the 2 equations, you can find the two x-intercepts and find that mid point of the 2 intercepts.
Now, you can get the slope, and a point... Use point-slope form to get the equation!~