Step-by-step explanation:
The parallel line will have an equation of the form
[tex]y = -\dfrac{1}{2}x + b[/tex]
We solve for b by plugging in the values of the point (3, -4):
[tex]-4 = -\dfrac{1}{2}(3) + b[/tex]
[tex]\Rightarrow -8 = -3 + 2b[/tex]
Solving for b, we get
[tex]b = -\dfrac{5}{2}[/tex]
Therefore, the equation of the line parallel to 2x + 4y = 10 is
[tex]y = -\dfrac{1}{2}x -\dfrac{5}{2}[/tex]
In standard form we can write
[tex]x + 2y = -5[/tex] or [tex]2x + 4y = -10[/tex]
