How do you find a standard form equation for the line with A (-1,4); Slope: 2/5?

Jul 19, 2017

$y - \frac{2}{5} x = 4 \frac{2}{5}$ which leads to

$2 x - 5 y = - 22$

Explanation:

The standard form of a line is expressed in the following form
$A x + B y = C$, where $A , B \mathmr{and} C$ are integers

To find this form use the formula $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

substitute in the point and slope (m)

$\left(y - 4\right) = \frac{2}{5} \left(x - \left(- 1\right)\right) \text{ }$ or $\text{ } \left(y - 4\right) = \frac{2}{5} \left(x + 1\right)$

$y - 4 = \frac{2}{5} x + \frac{2}{5}$

$y = \frac{2}{5} x + \frac{2}{5} + 4$

$y = \frac{2}{5} x + 4 \frac{2}{5} \text{ }$ now put into standard form

Multiply by $5$ to clear the denominators

$5 y - \frac{\cancel{5} \times 2}{\cancel{5}} x = \cancel{5} \times \frac{22}{\cancel{5}}$

$5 y - 2 x = 22$

$\Rightarrow 2 x - 5 y = - 22$