Question

Please help!

Passes through (- 1, - 8) and perpendicular to x + 3y = - 6
What is the equation?

Answer 1

y = 3x - 5

Explanation:

1) First, place the given equation in slope-intercept form, represented by the formula
`y = mx +b`, to find the slope. Whatever
`m` or the coefficient of x-term is will be the slope. Isolate y in the equation:

`x + 3y = -6\\3y = -x -6\\y = -(1)/(3)x-2`

So, the slope of that line is
`-(1)/(3)`. Lines that are perpendicular have slopes that are opposite reciprocals, thus the slope of the new line will be 3.

2) Now, use the point-slope formula
`y-y_1 = m (x-x_1)` to find the equation of the new line. Substitute real values for the
`m`,
`x_1` and
`y_1` in the equation.

Since
`m` represents the slope, substitute
`-(1)/(3)` in its place. Since
`x_1` and
`y_1` represents the x and y values of one point the line passes through, substitute the x and y values of (-1,-8) into the formula as well. Then, isolate the y in the resulting equation to put the equation in slope-intercept form and find an answer:

`y-(-8) = 3 (x-(-1))\\y + 8 = 3(x+1)\\y + 8=3x + 3\\y = 3x -5`