# How do you find a standard form equation for the line with A(2, −4) and is parallel to the line 5x-2y=4?

Jun 16, 2016

The desired line is $5 x - 2 y - 18 = 0$

#### Explanation:

A line parallel to $A x + B y + C = 0$ will always be of the form

$A x + B y + k = 0$.

Hence a line parallel to $5 x - 2 y = 4$ would be $5 x - 2 y + k = 0$

Putting the values of point $\left(2 , - 4\right)$ in this, we get

$5 \times 2 - 2 \times \left(- 4\right) + k = 0$ i.e.

$10 + 8 + k = 0$ or $k = - 18$

Hence equation is $5 x - 2 y - 18 = 0$