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Umnica [9.8K]
3 years ago
15

Write an equation of the line that is parallel to y = 1 2 x + 3 and passes through the point (10, -5). A) y = 2x - 15 B) y = -2x

+ 15 C) y = - 1 2 x Eliminate D) y = 1 2 x - 10
Mathematics
1 answer:
Annette [7]3 years ago
6 0

Answer:

<h2>B) y = -2x + 15</h2>

Step-by-step explanation:

\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\k\ \parallel\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\=============================\\\\\text{We have the equation}\ y=\dfrac{1}{2}x+3\to m_1=\dfrac{1}{2}.\ \text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{We have the equation}\ y=-2x+b\\\\\text{Put the coordinates of the point (10, -5) to the equation and solve}\\\text{for}\ b:\\\\-5=-2(10)+b\\-5=-20+b\qquad\text{add 20 to both sides}\\15=b\\\\\text{Finally we have:}\\\\y=-2x+15

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