Finding Equation of Curve to Touch Straight Line

[JonnyMontana]

Can anyone help as it's a long time since I studied this:

I have a straight line - which I have the equation for and a plotted curve with multiple points.

I want to figure out the point where the curve would touch the line shold it be moved toward the line.

I've tried using excel to get the equation of the line for the curve but it won't seem to select all the points and is not giving me a good equation.

Any advice apprecaited!

 

[HallsofIvy]

If you were to move the line to the curve, or the curve to the line (I presume you mean moving it "parallel to itself", without changing its orientation), they would first touch at a point at which the line is tangent to the curve.

So: determine the slope of the line. Differentiate the function determining the curve and set the derivative (slope of the tangent line), as a function of x, equal to the slope of the given line. Solve that equation for x.

 

[JonnyMontana]

Thanks.

Suppose we were to imagine that I'm a bit rusty with this can I ask a further question?

What is the best way for me to derive the equation of the curve?

If I give the simple details it may help.

Straight Line Equation
Y = 1022.7X + 115583 (I think!)
Points
9.0, 129150
11.0, 134000

Curve Points
29.6 77023
29.6 78363
29.6 79033
29.6 79703
29.6 80373
29.7 81043
29.7 81713
29.8 82383
29.9 83053
30.0 83723
30.2 84393
30.4 85063
30.7 85733
31.0 86403
31.3 87073
31.7 87743
32.2 88413
32.8 89083
33.4 89753
34.1 90423
34.9 91093
35.7 91763
36.7 92433
37.7 93103
38.9 93773
39.9 94282

Any advice appreciated!