What is the method for finding the mid-line of two parallel slopes?

[Windseaker]

I have a question:

If you have two slope lines that don't touch but are parallel, how do you find the middle slope line of the two?

 

[Mentallic]

Do you mean a 3rd line that is parallel to the other two, and equidistant from them?

Consider that you can find the x or y intercept of any line ax+by+c=0.

 

[Windseaker]

sorry i did not explain correctly
I am trying to find a line ( an average line) between two sloping lines that are parallel (but are just a little different from each other). I am trying to find that mid or average of the two.

 

[Windseaker]

OK let me try this:

I have two median lines, but I need to find the median line of two median lines!

 

[Mentallic]

sorry i did not explain correctly
I am trying to find a line ( an average line) between two sloping lines that are parallel (but are just a little different from each other). I am trying to find that mid or average of the two.

The average or middle of two parallel lines is exactly what I said, another parallel line but with the average value of the both. For example, at x=0, if the y intercept of the first line is 1 and the intercept of the second line is 3, then the average of the two will be 2=(1+3)/2

 

[BloodyFrozen]

I have a question:

If you have two slope lines that don't touch but are parallel, how do you find the middle slope line of the two?

Take the midpoint of the endpoints to both lines. Then use the slope formula to find the slope. If needed, plug in a point on the line to solve for b.

 

[HallsofIvy]

The question is what do you mean by "find the middle slope line"?

Geometrically: At any point on one of the two given lines, construct the perpendicular to that line. Because the two given lines are parallel this will also be perpendicular to the second line. The midpoint of that perpendicular is a point on the "middle slope line". Finding two such points gives you the line.

Algebraically: If one line is given by y= mx+ a, then the second line must be y= mx+ b. The "middle slope line" is y= mx+ (a+b)/2.