# What is the equation of the line passing through (1,2) with slope m= -5 ?

Jun 21, 2018

$y = - 5 x + 11$

#### Explanation:

The equation of a line is $y = m x + c$. We are given the value for $m$, $m = - 5$.
We can substitute this into the equation $y = m x + c$ to get $y = - 5 x + c$
We are also given the point $\left(1 , 2\right)$
This means when $y = 1$, $x = 2$
We can use this information to substitute it into our line formula to get $1 = - 5 \left(2\right) + c$
From this we can work out what c would be (by rearranging)
$1 = - 10 + c$ then turns into $1 + 10 = c = 11$, which we can then substitute into out original formula to get $y = - 5 x + 11$ or $11 - 5 x - y = 0$