# How do you write the equation of the line through (-1, -2) with slope of 1/2?

Apr 11, 2016

$y = \frac{1}{2} x - \frac{5}{2}$

#### Explanation:

Standard form$\text{ } y = m x + c$

Where m is the gradient (slope)

$\implies y = \frac{1}{2} x + c$

But we are told that this line passes through the point
$\left(x , y\right) \to \left(- 1 , - 2\right)$ so we can substitute these values to find the value of c

$\implies - 2 = \frac{1}{2} \left(- 1\right) + c$

$\implies - 2 = - \frac{1}{2} + c$

Add $\frac{1}{2}$ to both sides

$\implies - 2 + \frac{1}{2} = - \frac{1}{2} + \frac{1}{2} + c$

$\implies - 2 \frac{1}{2} = 0 + c$

So $c = - \frac{5}{2}$

Giving

$y = m x + c \text{ "->" } y = \frac{1}{2} x - \frac{5}{2}$