Question

What is the equation of the line perpendicular to Y-3x+1 that passes through the point (12,-6)?

y=x+1
3x + 2y = 24
3x + 2y = 6
2x - 3y = 42
2x - 3y = -48
Help plsss

Answer 1

It's A.

Explanation:

Edge 2020;)

Answer 2

`3y + x = -6`

Explanation:

Given

y = 3x + 1

Required

Equation of line that passes through (12,-6) and is perpendicular to y = 3x + 1

First, the slope of the line has to be calculated;

Th slope of a line is the coefficient of x in its linear equation;

This implies that the slope of y = 3x + 1 is 3

Having calculated the slope of the first line;

The relationship between both lines are perpendicularity; this implies that
`m_1 * m_2 = -1`

Where m_1 = 3 and m_2 is the slope of the secodnd line

`m_1 * m_2 = -1` becomes

`3 * m_2 = -1`

Divide both sides by 3

`(3 *m_2)/(m_2) = (-1)/(3)`

`m_2 = (-1)/(3)`

The equation of the line can be calculated using the folloing formula

`m = (y - y_1)/(x - x_1)`

Where
`(x_1, y_1) = (12,-6)` and
`m_2 = (-1)/(3)`

The equation becomes

`(-1)/(3) = (y -- 6)/(x - 12)`

`(-1)/(3) = (y + 6)/(x - 12)`

Cross multiply

`-(x - 12)= 3(y + 6)`

`-x + 12=3y + 18`

Collect like terms

`12 - 18 = 3y +x`

`-6 = 3y + x`

`3y + x = -6`