Question

What is the equation of the line perpendicular to y=2/3x+1 that passes through the point (12,-6)

Answer 1

Since our line is perpendicular to the function given, we can use that slope to find the slope of our new line.

To find the perpendicular slope, take the negative reciprocal of the original slope (negative and flip the fraction) so the slope of the new line will be -3/2.

y+6=-3/2(x-12)

There's your answer :)

Answer 2

`y+6=-1.5(x-12)` or
`y=-1.5x+12` or
`3x+2y=24`

Explanation:

we know that

If two lines are perpendicular, then the product of their slopes is equal to minus one

so

`m1*m2=-1`

Step 1

In this problem we have

the given line

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

The slope of the given line is

`m1=(2)/(3)`

Find the perpendicular slope m2

substitute in the formula

`(2)/(3)*m2=-1`

`m2=-(3)/(2)=-1.5`

Step 2

Find the equation of the line

we have

`m=-1.5`

`point(12,-6)`

The equation of the line into point slope form is equal to

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

substitute

`y+6=-1.5(x-12)` -------> equation of the line into point slope form

`y=-1.5x+18-6`

`y=-1.5x+12` ------> equation of the line into slope intercept form

The equation of the line in standard form is

`Ax+By=C`

`y=-1.5x+12`

`1.5x+y=12` -----> multiply by
`2`

`3x+2y=24` -----> equation of the line in standard form