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ali015
The easiest way to find a parallel equation is to write your equation in slope-intercept form. The general equation for slope-intercept form is y = mx + b, where m = the slope of the equation, b = the y intercept, and x and y are your variables.

You're given 5x + 10y = -4. 
1) Move 5x to the right side by subtracting 5x from both sides:
5x + 10y = -4
10y = -5x - 4

2) Divide both sides by 10 to get y by itself on the left. Simplify:
[tex]10y = -5x - 4\\ y = - \frac{5}{10} x - \frac{4}{10} \\ y = - \frac{1}{2} x - \frac{2}{5} [/tex]



Remember that for parallel lines, the slope, m, is the same for both equations. You can make the y-intercept, b, whatever number you want.

When the equation is in slope-intercept form, [tex]y = - \frac{1}{2} x - \frac{2}{5} [/tex], you can see that [tex] m = - \frac{1}{2}[/tex]. 

A parallel equation is in the form: 
[tex]y = - \frac{1}{2} x + b[/tex]

Plug in anything you want for b. One example is: [tex]y = - \frac{1}{2} x + 3[/tex]

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Answer: [tex]y = - \frac{1}{2} x + 3[/tex] (just one example)



MalakMselg
In case of parallel lines
[tex]\frac{a1}{a2} = \frac{b1}{b2} \: not \: equal \: to \: \frac{c1}{c2} [/tex]
Where a1, b1 and c1 are the constants of the first equation and a2, b2 and c2 are the constants of the second equation
From first equation (5x+10y+4 = 0)
a1 = 5
b1 = 10
c1 = 4
So now what we want to do is to divide 5 by a number and 10 by another number to get the same result at the end
I'll divide 5 by 1 and 10 by 2 to get the same number 5
5/1 = 10/2
Then I'll divide 4 by any number to get a result other than 5
Let's say 4 (or any other number it can be positive as well as negative)
So
a2 = 1
b2 = 2
c2 = 4
Then now the last step is to write the equation using these constants
x + 2y +4 =0
x+2y= - 4
Therefore this equation is parallel to 5x+10y = - 4

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