The equation of a line that passes through the points (-4, 47) and (2, -16) is 21x + 2y - 10 = 0.
The standard form of a line is ax + by + c = 0. If the line passes through the points (x1, y1) and (x2, y2), the equation of the line is evaluated by
y - y1 = [(y2 - y1)/(x2- x1)] · (x - x1)
The given points are (-4, 47) and (2, -16).
The equation of the line that passes through these points is
y - 47 = (-16 - 47)/(2 + 4) × (x + 4)
⇒ y - 47 = -63/6 × (x + 4)
⇒ 6(y - 47) = -63(x + 4)
⇒ 6y - 282 = -63x - 252
⇒ 63x + 6y = 282 - 252 = 30
⇒ 21x + 2y = 10
Therefore, the required standard form of the line that passes through the given points is 21x + 2y - 10 = 0.
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