Question

Perpendicular to Y equals 2X +4; Passing through the point (three, five). The line equation is Y=

Answer 1

`y=-(1)/(2)x+(13)/(2)`

Explanation:

step 1

Find the slope of the given line

we have

`y=2x+4`

the slope m is equal to

`m=2`

step 2

Find the slope of the perpendicular line to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

`m_1*m_2=-1`

we have

`m_1=2`

`(2)*m_2=-1`

`m_2=-(1)/(2)`

step 3

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=-(1)/(2)`

`point\ (3,5)`

substitute

`y-5=-(1)/(2)(x-3)`

Convert to slope intercept form

`y=mx+b`

`y-5=-(1)/(2)x+(3)/(2)`

`y=-(1)/(2)x+(3)/(2)+5`

`y=-(1)/(2)x+(13)/(2)`