Answer:
⅕
Step-by-step explanation:
Given that points X, Y, and Z are collinear, and X is said to partition segment XZ in the ratio XY to XZ = 1:5, it means that segment XY = ⅕ of XZ. That is XY/XZ = ⅕
See attachment below to understand how point Y divides segment XZ.
Therefore, the k value Brianna would use when solving the problem should be the fraction, ⅕.
k value = XY/XZ = 1/5
The point (2, 5) is not on the curve; probably you meant to say (2, -5)?
Consider an arbitrary point Q on the curve to the right of P, , where
. The slope of the secant line through P and Q is given by the difference quotient,
where we are allowed to simplify because .
Then the equation of the secant line is
Taking the limit as , we have
so the slope of the line tangent to the curve at P as slope 2.
- - -
We can verify this with differentiation. Taking the derivative, we get
and at , we get a slope of
, as expected.