How do you write an equation of a line passing through (-3, 5), perpendicular to #4x + 2y = 5#?

1 Answer
Apr 16, 2017

Answer:

#"the equation of line can be written as : "#
#color(blue)(y=1/2x+13/2)" or "#
#color(blue)(-x+2y=13)#

Explanation:

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#4x+2y=5#

#"First,let us rearrange the equation above to find slope of the line."#

#color(red)(2y=-4x+5)#

#color(red)(y=-(4x)/2+5/2)#

#color(red)(y=-2x+5/2)#

#"in equation y=m x+n,the coefficient of the term x gives"#
#"the slope of the line."#

#"The slope of the red line is "m_r=-2.#

#"İf two line are perpendicular each other,the product of their "##"slopes is -1."#

#m_b*m_r=-1#

#m_b:"the slope of the blue line"#
#m_r:"the slope of the red line."#

#m_b*(-2)=-1#

#m_b=1/2#

#"Since the slope and one point is known,the equation of the blue"##"line can be written."#

#y-y_1=m(x-x_1#

#m=m_b=1/2#

#P(-3,5) " ; "x_1=-3" , "y_1=5#

#color(blue)(y-5=1/2(x+3))#

#color(blue)(y=1/2(x+3)+5)#

#color(blue)(y=1/2x+3/2+5)#

#color(blue)(y=1/2x+13/2)#

#"Or "#

#color(blue)(-x+2y=13)#