Question

Write the equation of the line that is perpendicular toy= =-1/2x +11 and passes through the point(-10,1).

Answer 1

y = 2x + 21

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = -
`(1)/(2)` x + 11 ← is in slope- intercept form

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

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(2) )` = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (- 10, 1 ) into the partial equation

1 = - 20 + c ⇒ c = 1 + 20 = 21

y = 2x + 21 ← equation of perpendicular line

Answer 2

You have the following equation of a line:

`y=-(1)/(2)x+11`

In order to find the equation of a line perpendicular to the previous one, you take into account that the relation between the slopes of both lines is as follow:

`m_(1\cdot)m_2=-1`

You have that the slope of the first line is m1 = -1/2. By using the previous equation you can find the slope of the second slope, just as follow:

m₂ = -1/(m₁) = -1/(-1/2) = 2

In order to find the equation of the second line, you use the following formula:

m₂ = (y - yo)/(x - xo)

where m2 is the slope of the second line, and (xo,yo) is a point with specific coordinates. You have that the second line passes trough the point (-10,1), then, by replacing into the last expression, you can solve for m, just as follow:

m₂ = (y - 1)/(x - (-10))

m₂ = (y - 1)/(x + 10)

(x + 10) m₂ = y - 1

m₂x + 10m₂ + 1 = y

(2)x + 10(2) + 1 = y

2x + 20 + 1 = y

2x + 21 = y

Hence, the equation of the second line is:

y = 2x + 21