Question

Given line has the equation 2X +12 Y equals negative one what is the equation in slope intercept form of the line that is perpendicular to the given line and passes through the point (0,9)? y=( ) x+9

Answer 1

y = 12x + 9 is the answer.

Explanation:

Since the given equation is 2x + 12 y = -1

12y = -2x -1

`y=-(1)/(12)(2x+1)`

`y=-(1)/(12)x-(1)/(12)`

Now this line is in the form of y = mx + c

Here m = slope = -1/12

We have to calculate the slope of another line perpendicular to this line and passing through (0, 9).

Let the equation is y = m' + c'

We know m×m' = -1 for two perpendicular lines

`-((1)/(12))(m')=-1`

m' = 12

Therefore the equation will be

y = 12x + c'

Since this line passes through ( 0, 9)

9 = 12×0 + c'

c' = 9

Now the equation will be

y = 12x + 9

This is the answer.

Answer 2

y = 6x+9

Explanation:

We have given an equation.

2x+12y=-1 eq(1)

y = mx+c is slope-intercept form of equation of line where m is slope and c is y intercept.

We can write eq(1) in slope-intercept form:

12y = -2x-1

y = 1/12(-2x-1)

y = -1/6x-1/12

let m₁ is slope of given line which is equal to -1/6.

Perpendicular lines have slopes negative reciprocals of each other.

Let m₂ is slope of perpendicular line.

m₂ = 6 and we have given y-intercept = 9.

Putting the value of c and m₂ in slope-intercept form of equation, we have

y = 6x+9 is slope-intercept of line that is perpendicular to the given line and passes through the point (0,9).