# How do you write an equation of the line parallel to the line 10x - 5y = 8 and passing through the point (2,4)?

Mar 21, 2018

The equation the line is $2 x - y = 0$

#### Explanation:

The equation of a line is 10x-5y-8=0; (1)

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

parallal to $10 x - 5 y - 8 = 0$ is 10x-5y+c=0 ; (2) The point

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

$\therefore 10 \cdot 2 - 5 \cdot 4 + c = 0 \mathmr{and} 20 - 20 + c = 0 \therefore c = 0$

So , the equation the line is

$10 x - 5 y + 0 = 0 \mathmr{and} 10 x - 5 y = 0 \mathmr{and} 2 x - y = 0$ [Ans]