Find a b c and d when the curve y=ax^3+bx^2+cx+d touches the line y=x+1 at point 0,1 and the line y=-2x+10?

"touches the line y=x+1 at point 0,1"
Two pieces of information here.
1. When x = 0, y = ax^3 + bx^2 + cx + d = 1. Plug in x = 0 and y = 1 and see what that tells you.
2. The slope at x = 0 is the same as the slope of y = x + 1, which is 1. Take the derivative of ax^3 + bx^2 + cx + d and set x = 0 and slope = 1 and see what that tells you.

"and the line y=-2x+10..."
This was no doubt going to be similar information. Plug in the given values of x and y and the slope of y, and see what that tells you.

2. The slope at x = 0 is the same as the slope of y = x + 1, which is 1. Take the derivative of ax^3 + bx^2 + cx + d and set x = 0 and slope = 1 and see what that tells you.

Can u show it step by step? thx for your help:))