The equation of line that is perpendicular to the given equation and passes through the given point is y = -3x - 2.
Given the equation of line and point;
First, find the slope intercept form ( y = mx + b )of the given equation to determine the slope.
−2x + 6y = −1
Solve for y
6y = 2x - 1
y = (2/6)x - 1/6
y = (1/3)x - 1/6
Hence, the slope m = 1/3
Now, the equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Slope of the perpendicular will be;
m_perpendicular = -3
Next, find the equation of the perpendicular line using the point slope formula y - y₁ = m( x - x₁ ).
Plug in the slope m = -3 and the point (-2,4).
y - y₁ = m( x - x₁ )
y - 4 = -3( x - (-2) )
y - 4 = -3( x + 2 )
y - 4 = -3x - 6
y = -3x - 6 + 4
y = -3x - 2
Therefore, the equation of line that is perpendicular to the given equation and passes through the given point is y = -3x - 2.
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