# How do you find k so that the line through (k,k+1) and (2,3) will have a slope of -1?

Sep 15, 2015

I could not find $k$!

#### Explanation:

Consider the general relationship that gives you the slope $m$ as:
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ (1)
Let us use our data:
$- 1 = \frac{3 - \left(k + 1\right)}{2 - k}$ and solve for $k$:
$k - 2 = 3 - k - 1$
$k + k = 3 + 2 - 1$
$2 k = 4$
so $k = \frac{4}{2} = 2$
BUT if you try this solution into your slope (equation 1) it doesn't work.
So I think it is not possible to have a line with this slope...