# Find an equation of the line

1. Oct 1, 2009

### sml92

1. The problem statement, all variables and given/known data

Function: f(x)=x^2-x Line: x+2y-6=0

3. The attempt at a solution
Find an equation of the line that is tangent to the graph of f and parallel to the given line.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 2, 2009

### rootX

What is the requirement for two lines to be parallel to each other?

3. Oct 2, 2009

### RPierre

First, you must simplify your line for y = mx + b form.

x + 2y - 6 = 0

-> x - 6 = -2y

-> $$\frac{x-6}{-2}$$ = y

-> y = $$\frac{-1x}{2}$$ + 3

Next, to find a line tangent to f(x), we take it's derivitive

f'(x) = 2x - 1

Compare the two slopes. 2 and -1/2. These are in fact perpendicular to each other. See what you can do with that.

4. Oct 2, 2009

### Dick

I think you should rethink that. I see a line with slope -1/2 and another line with a variable slope. Perhaps you should equate them.

5. Oct 4, 2009

thanks guys