# Question #aa9ba

Apr 6, 2017

$3 y - 4 x + 39 = 0$

#### Explanation:

THE POINT SLOPE FORM:-
if a line passes through a point $\left(a , b\right)$ and has a slope $m$ the its equation can be written in point slope form as follows:-
$\textcolor{red}{y - b = m \left(x - a\right)}$

In the given problem;
1. $\left(a , b\right) = \left(9 , - 1\right)$
2. $m = \frac{4}{3}$
$\therefore$ the equation of this line becomes
$y - \left(- 1\right) = \frac{4}{3} \cdot \left(x - 9\right)$
$\implies 3 \cdot \left(y + 1\right) = 4 \cdot \left(x - 9\right)$
$\implies 3 y + 3 = 4 x - 36$
$\implies \textcolor{red}{3 y - 4 x + 39 = 0}$ is the required equation

Apr 6, 2017

$y + 1 = \frac{4}{3} \left(x - 9\right)$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here " m=4/3" and } \left({x}_{1} , {y}_{1}\right) = \left(9 , - 1\right)$

$\Rightarrow y - \left(- 1\right) = \frac{4}{3} \left(x - 9\right)$

$\Rightarrow y + 1 = \frac{4}{3} \left(x - 9\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$