Question

BEDE

Which of the following equations represents a line that is perpendicular to
Y = -4x+9 and passes through the point, (4, 5)?

A. y =1/4×+6
B. y = 3x+4
C. y = 1/4×+5
D. y = -4x+ 4​

Answer 1

`\large\boxed{y=(1)/(4)x+4}`

Explanation:

`Let:\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2\\============================\\\\\text{We have the equation of the line:}\ y=-4x+9\to m_1=-4.\\\\\text{Therefore}\ m_2=-(1)/(-4)=(1)/(4).\\\\\text{Put the value of the slope and the coodrdinates of the given point (4, 5)}\\\text{to the equation of a line}\ y=mx+b:\\\\5=(1)/(4)(4)+b\\\\5=1+b\qquad\text{subtract 1 from both sides}\\\\4=b\to b=4\\\\\text{Finally:}\\\\y=(1)/(4)x+4`