The equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.
Slope of the line KL = (8 - 0)/(-6 - 6) = 8/(-12) = -2/3.
Using the formula of the slope of the line passing through the points (x₂, y₂) and (x₁, y₁), as m = (y₂ - y₁)/(x₂ - x₁).
The slope of the line parallel to the line KL will be equal to the slope of KL.
Thus, the slope of the required line is m = -2/3.
The required line also passes through point M (-4, -2).
Thus, the equation of the required line will be,
y - (-2) = (-2/3)(x - (-4)) {Using the equation of the line passing through the point (x₁, y₁) and a slope m, as y - y₁ = m(x - x₁)},
or, y + 2 = (-2/3)(x + 4),
or, 3(y + 2) = -2x - 8,
or, 2x + 3y = -6.
From the given points, only the point (-6, 2) satisfies the equation.
Thus, the equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.
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The provided question is incomplete. The complete question is:
"On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M?
(–10, 0)
(–6, 2)
(0, –6)
(8, –10)"
