# How do you write an equation of a line given point (1,-5) and slope -3/2?

Sep 4, 2016

$y = - \frac{3}{2} x - \frac{7}{2}$

#### Explanation:

We can begin by writing the equation in $\textcolor{b l u e}{\text{point-slope form}}$

That is $\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

here $m = - \frac{3}{2} \text{ and } \left({x}_{1} , {y}_{1}\right) = \left(1 , - 5\right)$

substitute these values into the equation.

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

distribute the bracket and collect like terms

$y + 5 = - \frac{3}{2} x + \frac{3}{2} \Rightarrow y = - \frac{3}{2} x - \frac{7}{2} \text{ is the equation}$