The slope of a line (m) is defined as rise (change in y values) over run (change in x values). Mathematically, the slope can be described as: m = (y2 - y1)/(x2 - x1)
For this question, you can label the points 1 (6,9) and 2 (-3,9). This means that x1=6, y1=9, x2=-3, and y2=9. From there,...
To deal with the 1 in this integral, you can break up the original integral as follows:
∫[1+√(9-x^2)]dx = ∫1dx + ∫√(9-x^2)dx
*Note: I have indicated these as indefinite integrals because there is no way to nicely format definite integrals on here.
If the equation is as written and the two equal signs are not typing errors, the equation would be considered unsolvable or false. If this is a typo, I can show you how to solve for the variable 'k' if you post the corrected form of the equation.
To answer your follow up question:
He took the derivative of both sides of the equation tan y = x.
The derivative of tan y = sec^2(y) y' and the derivative of x = 1
So, you get sec^2(y) y' = 1, and then you can solve for y'