Answer :
Answer:
y = 3x - 5
Step-by-step explanation:
1) First, place the given equation in slope-intercept form, represented by the formula [tex]y = mx +b[/tex], to find the slope. Whatever [tex]m[/tex] or the coefficient of x-term is will be the slope. Isolate y in the equation:
[tex]x + 3y = -6\\3y = -x -6\\y = -\frac{1}{3}x-2[/tex]
So, the slope of that line is [tex]-\frac{1}{3}[/tex]. 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 [tex]y-y_1 = m (x-x_1)[/tex] to find the equation of the new line. Substitute real values for the [tex]m[/tex], [tex]x_1[/tex] and [tex]y_1[/tex] in the equation.
Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{1}{3}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] 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:
[tex]y-(-8) = 3 (x-(-1))\\y + 8 = 3(x+1)\\y + 8=3x + 3\\y = 3x -5[/tex]