# Point of slope at certain distance

1. Sep 8, 2008

### duki

Hey Everyone,

Another question for you. Is there a way to find the point on a slope at a certain distance? For example, suppose I had a slope that was previously calculated from point A to point B. I want to find at what point Y is at distance X. Does that make sense?

2. Sep 8, 2008

### rootX

Linear equation?

y = ax+b

you can get it from point A and B.

Slope's not a good work in my opinion. It means finding a point on dy/dx ....

3. Sep 8, 2008

### Dick

No, it doesn't really make sense. What's the real question?

4. Sep 8, 2008

### duki

a being point A and b being point B?

5. Sep 8, 2008

### duki

edit: my example doesn't work. I'll post a new example shortly

6. Sep 8, 2008

### Dick

Find the equation of the line from A to B and then intersect it with a circle around A of radius X. Is that what you mean? I'm still guessing.

7. Sep 8, 2008

### duki

Ok here's a more precise example:

I need to calculate the slope from elevation A to elevation B from X1 to X2. Once the slope is determined, the user inputs a distance X3 and a new elevation.

I need to find the distance between the new elevation and the elevation at point X3 of the original slope.

Example:

Find slope from y = 1720.85 feet to y = 1738.34 feet (which starts at x = 2 feet and ends at x = 82 feet).
Plot this line
The user inputs a new distance, in this example 64 feet, and a new elevation at 64, 1736.54.
I need to find the distance between this point (on the new elevation) and the same point (64) on the original slope from A to B.

Does that make sense?

8. Sep 8, 2008

### Dick

That makes perfect sense. Thanks. Why don't you just write an equation for the line whose slope you have computed, i.e. y=m*x+b. Then you just need to compute the vertical distance from new elevation to m*X3+b.

9. Sep 8, 2008

### duki

Thanks for the help.
I'm a little confused.

I got a slope of .2186
Then I do y = .2186(64)+b?

10. Sep 9, 2008

### Dick

b is the y-intercept. It value of b that solves .2186*2+b=1720.85. It's just finding the equation of a line through two points. Can you review that?

11. Sep 9, 2008

### duki

I think I did something wrong. I got a distance of 2.1368

$$b=1720.85-.2186*2$$
$$b=1720.4128$$
$$b2=1736.10-.2186*64$$
$$b2=1722.5496$$

$$d = b - b2$$
$$d = 2.1368$$

12. Sep 9, 2008

### Dick

If b and b2 are different, it's only because you are rounding off the slope to four decimal places. 1720 and 1736 aren't that different. Try keeping more accuracy around.