# How do you find a equation of the line containing the given pair of points (-5,0) and (0,9)?

Jul 9, 2015

I found: $9 x - 5 y = - 45$

#### Explanation:

I would try using the following relationship:

$\textcolor{red}{\frac{x - {x}_{2}}{{x}_{2} - {x}_{1}} = \frac{y - {y}_{2}}{{y}_{2} - {y}_{1}}}$

Where you use the coordinate of your points as:
$\frac{x - 0}{0 - \left(- 5\right)} = \frac{y - 9}{9 - 0}$
rearranging:
$9 x = 5 y - 45$
Giving:
$9 x - 5 y = - 45$

Jul 9, 2015

$y = \left(\frac{9}{5}\right) \cdot x + 9$

#### Explanation:

You are searching the equation of a straight line (=linear equation) who contain $A \left(- 5 , 0\right) \mathmr{and} B \left(0 , 9\right)$

A linear equation form is : $y = a \cdot x + b$, and here we will try to find numbers $a$ and $b$

Find $a$ :

The number $a$ representing the slope of the line.

$a = \frac{{y}_{b} - {y}_{a}}{{x}_{b} - {x}_{a}} = {\Delta}_{y} / {\Delta}_{x}$

with ${x}_{a}$ representing the abscissa of the point $A$ and ${y}_{a}$ is the ordinate of the point $A$.

Here, $a = \frac{9 - 0}{0 - \left(- 5\right)} = \frac{9}{5}$

Now our equation is : $y = \left(\frac{9}{5}\right) \cdot x + b$

Find $b$ :

Take one point given, and replace $x$ and $y$ by the coordinate of this point and find $b$.

We are lucky to have one point with $0$ in abscissa, it makes the resolution easier :

${y}_{b} = \left(\frac{9}{5}\right) \cdot {x}_{b} + b$
$9 = \left(\frac{9}{5}\right) \cdot 0 + b$
$b = 9$

Therefore, we have the equation line !

$y = \left(\frac{9}{5}\right) \cdot x + 9$