The equation of line which passes through point (-1, -8) and slope 3 is y = 3x -5.
The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
Here, Line passes through (-1, -8) and perpendicular to x + 3y = -6
Given equation of line: x + 3y = -6
3y = -6 - x
y = (-6 -x)/3
y = (-1/3)x - 2
Slope of given line m₁ = -1/3
we know, if two lines are perpendicular the product of their slope is -1.
m₁.m₂ = -1
(-1/3) m₂ = -1
m₂ = 3
Equation of Line passing through point (-1, -8) and slope 3
(y - y₁) = m₂(x - x₁)
( y - (-8)) = 3(x - (-1))
(y + 8) = 3(x + 1)
y + 8 = 3x + 3
y = 3x + 3 - 8
y = 3x -5
Thus, the equation of line which passes through point (-1, -8) and slope 3 is y = 3x -5.
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