Question

Write an equation in slope intercept form that is perpendicular to 3x + 2y equals 12 and passes through the point (1,2)​

Answer 1

The equation is y = (2/3)x + (4/3).

Explanation:

First, you have to change the equation into slope-intecept formula to find its gradient (slope) :

`3x + 2y = 12`

`2y = - 3x + 12`

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

Given that when a line is perpendicular to the other line, their slope value multiplied, will form -1. Next, we have to find the slope for line :

`m1 * m2 = - 1`

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

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

`m2 = (2)/(3)`

Lastly, we have to subatitute the x and y values into the equation, to find its intercept value :

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

`let \: x = 1,y = 2`

`2 = (2)/(3) (1) + b`

`b = 2 - (2)/(3)`

`b = (4)/(3)`

`y = (2)/(3) x + (4)/(3)`