Question

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

Answer 1

B) y = -2x + 15

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=-(1)/(m_1)\\=============================\\\\\text{We have the equation}\ y=(1)/(2)x+3\to m_1=(1)/(2).\ \text{Therefore}\ m_2=-(1)/((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`