ANSWER
4x + 7y = -14
EXPLANATION
Two lines are parallel if they have the same slope. The slope of the given line is -4/7. The other lines are given in the standard form,
[tex]ax+by=c[/tex]
The slope when the equation is in this form is,
[tex]m=-\frac{a}{b}[/tex]
We have to find the equation that has the same slope as the given line.
• The slope of the first equation 7x + 4y = 32 is -7/4.
,
• The slope of the second equation 7x-4y = -12 is 7/4
,
• The slope of the third equation 7y - 4x = 7 is 4/7
,
• The slope of the fourth equation 4x + 7y = -14 is ,-4/7
Hence, the line that is parallel to the given line is 4x + 7y = -14
