Question

What is the equation of the line perpendicular to y=1/2x+6 that passes through the point (4, 1)?

A y=-2x+9
B y=-1/2x+3
C y=1/2x-1
Dy=2x-7

Answer 1

A. y = -2x + 9

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

Let
`k:y=m_1x+b_1,\ l:y=m_2x+b_2`

then

`l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2`

We have the equation of the line:

`y=(1)/(2)x+6\to m_1=(1)/(2)`

therefore a slope of a line perpendicular to given line has the slope:

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

Put the value of slope m = -2 and the coordinates of the point (4, 1) to the equation of a line:

`1=-2(4)+b`

`1=-8+b` add 8 to both sides

`9=b\to b=9`

Finally:

`y=-2x+9`

Answer 2

A

Explanation:

Find the slope of the perpendicular line.

The slopes are related by the formula

m1 * m2 = - 1

Since m1 is 1/2, m2 must be -2

So far what you have is y = -2x + b

Find the y intercept (b).

The new line goes through (4,1)

x = 4

y = 1

1 = -2(4) + b

1 = - 8 + b

b = 1 + 8

b = 9

The answer is

y = - 2x + 9