# The line through the points (-2,3) and (-1,k) has slope k. What is k?

Jul 31, 2018

$\text{For no "k," any line that passes through the points}$

$\left(- 2 , 3\right) \text{ and "(-1,k)" can have slope } k$.

#### Explanation:

The slope of line through the points $\left(- 2 , 3\right) \mathmr{and} \left(- 1 , k\right)$ is

$\frac{k - 3}{- 1 - \left(- 2\right)} = \left(k - 3\right) .$

But, this slope is given to be $k$.

$\therefore k - 3 = k \Rightarrow - 3 = 0 , \text{ which is impossible}$.

$\therefore \text{for no "k," any line that passes through the points}$

$\left(- 2 , 3\right) \text{ and "(-1,k)" can have slope } k$.