Write an equation parallel to the line

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:


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, , you can see that . 

A parallel equation is in the form: 


Plug in anything you want for b. One example is: 

-------

  (just one example)

In case of parallel lines

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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