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19 votes
Please help!

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

User Remy Vanherweghem
by
2.8k points

1 Answer

14 votes
14 votes

Answer:

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

User EPascoal
by
3.2k points