Explanation

To find the slope of the tangent to the parabola y = 2x^2 - 13x + 5, we need to find the derivative of y with respect to x.

dy/dx = 4x - 13

We want to find if there is a point where the slope of the tangent is -1.

4x - 13 = -1

4x = 12

x = 3

Now, we need to find the corresponding y-coordinate.

y = 2(3)^2 - 13(3) + 5

y = 18 - 39 + 5

y = -16

So, the point of tangency is (3, -16).

The equation of the tangent line is:

y - (-16) = -1(x - 3)

y + 16 = -x + 3

y = -x - 13