Question

A. y=4x+3
B. y=-2x+3
C. y=-x+3
D.y=2x+3

Answer 1

y = -x + 3

Explanation:

`\text{Let:}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\\text{then}\\\\k\ ||\ 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 of a line}\\\\k:y=x-1\to m_1=1\\\\\text{Therefore}\\\\m_2=-(1)/(1)=-1\\\\\text{Initially, our equation has the form}\\\\y=-1x+b\Rightarrow y=-x+b`

`\text{The line should pass through point (5, -2).}\\\text{We substitute the coordinates of the point into the equation:}\\\\-2=-5+b\qquad\text{add 5 to both sides}\\\\-2+5=-5+5+b\\\\3=b\to b=3\\\\\text{Finally:}\\\\y=-x+3`