Calculate and show the intersection of two curves

[Bob Wen]

I draw two functions on a graph:
graph twoway (function y=x^(-0.5)) (function y=8-(1/3)*x). I want to know how to calculate and show the coordinates of the intersection of these two curves. Thank you!

[Carole J. Wilson]

You can set the two functions equal and solve for x by hand. Since you have a polynomial, you might end up with multiple values of x. You can then substitute each x in one of the original equations to get a y coordinate for each.

I started working by hand and then gave up because it was looking messy. I instead used an online equation solver (https://www.mathpapa.com/equation-solver/) to get the x coordinates by solving for x in the following:

x^{-\frac{1}{2}}=8-\frac{1}{3}x

Then I substituted the x values into the first function yielding the matching y coordinates.

When graphing the functions, use the -range()- option to show all intersections (fill in the ?? with the range you want):

graph twoway (function y1=x^(-0.5), range(?? ??) n(10000)) (function y2=8-(1/3)*x , range(?? ??) n(10000))

I increased the number of points that are graphed with -n(10000)- so that both graphs show enough points to clearly show the intersections. It is necessary in this case.

[Bob Wen]

Thank you so much Wilson!