# What is the equation of the line that passes through the point (4,-5) and is parallel to 2x-5y= -10?

Apr 3, 2018

The equation of line passing through $\left(4 , - 5\right)$ , parallal to
$2 x - 5 y = - 10$ is $2 x - 5 y = 33$

#### Explanation:

Parallal lines have equal slopes . Therefore the equation of a line

parallal to 2x-5y=-10;(1) is 2x-5y+c=0 ; (2) The point

$\left(4 , - 5\right)$ is on the line so , it will satisfy the equation (2).

$\therefore 2 \cdot 4 - 5 \cdot \left(- 5\right) + c = 0 \mathmr{and} 8 + 25 + c = 0 \therefore c = - 33$

So , the equation the line is $2 x - 5 y - 33 = 0 \mathmr{and} 2 x - 5 y = 33$

The equation of line passing through $\left(4 , - 5\right)$ , parallal to

$2 x - 5 y = - 10$ is $2 x - 5 y = 33$ [Ans]