# How do you write an equation in standard form for a line which passes through points (-10,3) and (-2,-5)?

May 11, 2015

The equation of the line is $y = - x - 7$.

To find this, note that we are looking for an equation of the form:

$y = m x + c$

for some constant slope $m$ and intercept $c$.

The slope $m$ can be calculated as:

$m = \frac{\Delta y}{\Delta x} = \frac{- 5 - 3}{- 2 - \left(- 10\right)} = \frac{- 8}{8} = - 1$

where $\Delta y$ means the change in $y$ and $\Delta x$ means the change in $x$.

So we now know that $y = m x + c = \left(- 1\right) x + c = - x + c$.

Add $x$ to both ends to get $y + x = c$. Subsitute in either of our points to calculate $c$. Let us use $x = - 10$ and $y = 3$:

$c = y + x = 3 + \left(- 10\right) = 3 - 10 = - 7$.

So $m = - 1$ and $c = - 7$, giving $y = - x - 7$.