# Question #273da

Sep 30, 2016

$- 7 x + 12 y = 21$

#### Explanation:

Assuming the question is to find the equation of the line passing through those two points:

Step 1: Find the slope of the line
The slope $m$ of a line passing through the points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by

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

Substituting the given points in, we get

$m = \frac{7 - 0}{9 - \left(- 3\right)} = \frac{7}{12}$

Step 2: Write the equation of the line in point-slope form
The point-slope form of a line with slope $m$ and passing through the point $\left({x}_{1} , {y}_{1}\right)$ is

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Substituting one of the given points and our slope, we get

$y - 0 = \frac{7}{12} \left(x - \left(- 3\right)\right)$

$\implies y = \frac{7}{12} \left(x + 3\right)$

Step 3: Convert the equation into standard form
The standard form of a line is $A x + B y = C$ where, if possible, $A , B ,$ and $C$ are integers without a common factor. We perform algebraic manipulations on the above equation until it matches this form.

$y = \frac{7}{12} \left(x + 3\right)$

$\implies y = \frac{7}{12} x + \frac{7}{4}$

$\implies - \frac{7}{12} x + y = \frac{7}{4}$

$\therefore - 7 x + 12 y = 21$