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B) If the line is parallel, that means the slope is the same.
The slope for the original line is
= 
.
The second form of coral line would be y = -1/4x + (any number). You could use y = -1/4x + 3.
c) Solve 12x = 24 + 3y for y.
3y = 12x - 24
y = 4x - 8
Perpendicular lines have negative reciprocal slopes... the negative reciprocal for -1/4 is 4. So yes, the third coral structure is perpendicular to the first coral.
The slope for the original line is
The second form of coral line would be y = -1/4x + (any number). You could use y = -1/4x + 3.
c) Solve 12x = 24 + 3y for y.
3y = 12x - 24
y = 4x - 8
Perpendicular lines have negative reciprocal slopes... the negative reciprocal for -1/4 is 4. So yes, the third coral structure is perpendicular to the first coral.