# How do you find the value of K so that the slope of the line through(2,-K) and (-1,4) is 1?

Jan 31, 2017

See the entire solution process below:

#### Explanation:

The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substitute the values given in the problem and solve for $K$:

$1 = \frac{\textcolor{red}{4} - \textcolor{b l u e}{- K}}{\textcolor{red}{- 1} - \textcolor{b l u e}{2}}$

$1 = \frac{4 + \textcolor{b l u e}{K}}{- 3}$

$\textcolor{red}{- 3} \times 1 = \textcolor{red}{- 3} \times \frac{4 + \textcolor{b l u e}{K}}{- 3}$

$- 3 = \cancel{\textcolor{red}{- 3}} \times \frac{4 + \textcolor{b l u e}{K}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}}}$

$- 3 = 4 + \textcolor{b l u e}{K}$

$- 3 - \textcolor{red}{4} = 4 + \textcolor{b l u e}{K} - \textcolor{red}{4}$

$- 3 - \textcolor{red}{4} = 4 - \textcolor{red}{4} + \textcolor{b l u e}{K}$

$- 7 = 0 + \textcolor{b l u e}{K}$

$- 7 = \textcolor{b l u e}{K}$

$\textcolor{b l u e}{K} = - 7$