(a) Find the slope m of the tangent to the curve y = 5/x at the point a where x = a > 0.m = (b) Find equations of the tangent lines at the points (1, 5) and 4, 52.y(x) =  (at the point (1, 5))y(x) = at the point 4, 52(c) Graph the curve and both tangents on a common screen.

It seems like there's a bit of confusion in your question. However, I'll try to answer it as best as I can.

(a) To find the slope of the tangent to the curve y = 5/x at the point where x = a > 0, we first need to find the derivative of y with respect to x. The derivative of y = 5/x is -5/x^2. So, the slope of the tangent line at x = a is m = -5/a^2.

(b) The equation of the tangent line to a curve at a given point can be found using the formula y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope of the tangent line.

For the point (1, 5), the slope of the tangent line is m = -5/1^2 = -5. So, the equation of the tangent line at this point is y - 5 = -5(x - 1), or y = -5x + 10.

For the point (4, 5/2), the slope of the tangent line is m = -5/4^2 = -5/16. So, the equation of the tangent line at this point is y - 5/2 = -5/16(x - 4), or y = -5/16x + 21/4.

(c) To graph the curve and both tangents on a common screen, you would plot the function y = 5/x and the two tangent lines y = -5x + 10 and y = -5/16x + 21/4. I'm sorry I can't provide a graph here, but there are many online graphing tools you can use to visualize these equations.