Question

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

Answer 1

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

Explanation:

`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)`