Question

Which of the following equations represents a line that is perpendicular to
y = -2x+4 and passes through the point, (4, 2)?

Answer 1

Answer:

$\large\boxed{y=\dfrac{1}{2}x}$

Step-by-step explanation:

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

$\text{We have the equation:}\ y=-2x+4\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{We have the equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinate of the point (4, 2) to the equation:}\\\\2=\dfrac{1}{2}(4)+b\\\\2=2+b\qquad\text{subtract 2 from both sides}\\\\0=b\to b=0.\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x$