# If c does not equal 0 and the slope of the line passing through (-c, 2c) and (4c, a) is 1, what is the expression for a in terms of c?

Sep 8, 2016

$a = 7 c$.

#### Explanation:

We know that the slope, say, $m$, of the line passing thro. pts.

$\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$ is given by,

$m = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}} , {x}_{1} \ne {x}_{2}$.

Therefore, in our case,

$\frac{2 c - a}{- c - 4 c} = 1 , c \ne 0$

$\therefore 2 c - a = - 5 c$

$\therefore 2 c + 5 c = a , \mathmr{and} ,$

$a = 7 c$.