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Write the equation of the line parallel to 4x-5y=2 and passing through point (0,0)

User Dkv
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k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2

We have:


4x-5y=2\ \ \ \ |-4x\\\\-5y=-4x+2\ \ \ \ |:(-5)\\\\y=(4)/(5)x-(2)/(5)\to m_1=(4)/(5)\\\\l:y=m_2x+b\\\\k\ \prep\ l\Rightarrow(4)/(5)m_2=-1\ \ \ \ |\cdot(5)/(4)\\\\m_2=-(5)/(4)


l:y=-(5)/(4)x+b

The line l is passing through point (0, 0). Substitute the coordinates of the point to the equation of a line l:


0=-(5)/(4)\cdot0+b\to b=0


y=-(5)/(4)x\ \ \ \ |\cdot4\\\\4y=-5x\ \ \ \ |+5x\\\\5x+4y=0

Answer: 5x + 4y = 0

User Gs Hurley
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