Mathematics: Bedewhich of the following equations represents a line that is perpendicular toy = -4x+9 and passes through the point, (4, 5)? a. y =1/4×+6b. y = 3x+4c. y = 1/4×+5d. y = -4x+ 4

Bedewhich of the following equations represents a

Ответ:

qorderiusnewton

12.03.2022

$\large\boxed{y=\dfrac{1}{4}x+4}$

Step-by-step explanation:

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