# Math Help - Finding a point P on a curve y=x^3

1. ## Finding a point P on a curve y=x^3

The question I have been struggling with is

Find P on the curve y-x^3 such that the slope of the line passing through P and (1,1) is 3/4

2. ## Re: Finding a point P on a curve y=x^3

Recall the slope of a line can be determined by $\frac{y_2-y_1}{x_2-x_1}$

In your case, solve for $x$ such that $\frac{3}{4} = \frac{x^3-1}{x-1}$

3. ## Re: Finding a point P on a curve y=x^3

Another way of doing this: a line passing through (1, 1) with slope 3/4 is of the form y- 1= (3/4)(x- 1) or y= (3/4)x+ 1/4. Solve that and $y= x^3$ simultaneously. Just replacing y in $y= x^3$ with (3/4)x+ 1/4 gives a cubic equation with a simple answer.