How do you find the values of k when the straight line y equals kx -2 is a tangent to the curve y equals x squared -8x plus 7?

By implication : x2-8x+7 = kx-2

Form a quadratic equation: x2-8x-kx+9 = 0

For a line to be a tangent to the curve it must have two equal roots and the discriminant b2-4ac of the quadratic equation must equal 0.

So: (-8-k)2-4*1*9 = 0

(-8-k)2-36 = 0

(-8-k)2 = 36

Square root both sides:

-8-k = -/+6

-k = 2 or 14

k = -2 or -14

When k = -2 is substituted into the quadratic equation x will have two equal roots of 3

When k = -14 is substituted into the quadratic equation x will have two equal roots of -3