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Which of the following equations represents a line that is parallel to y = 5x - 4
and passes through the point, (3, 4)?

1 Answer

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Answer:

y = 5x - 11

Explanation:


\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2\\\\==============================


\text{We have the equation:}\ y=5x-4\to m_1=5.\\\\\text{Therefore}\ m_2=5.\\\\\text{We have the equation:}\ y=5x+b.\\\\\text{Put the coordinates of the given point (3, 4) to the equation:}\\\\4=5(3)+b\\\\4=15+b\qquad\text{subtract 15 from both sides}\\\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=5x-11

User PatrickNolan
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