1
algebra

Which equation represents the line passing through (3,−2)(3, -2) with a slope of 4 in point-slope form?

A

y+2=4(x−3)y + 2 = 4(x - 3)

B

y−2=4(x+3)y - 2 = 4(x + 3)

C

y+2=4(x+3)y + 2 = 4(x + 3)

D

y−3=4(x+2)y - 3 = 4(x + 2)

Correct Answer: A

Choice A is the correct answer. Use the point-slope formula y−y1=m(x−x1)y - y_1 = m(x - x_1).

  1. Substitute: Let (x1,y1)=(3,−2)(x_1, y_1) = (3, -2) and m=4m = 4.
  2. Equation: y−(−2)=4(x−3)y - (-2) = 4(x - 3).
  3. Simplify: y+2=4(x−3)y + 2 = 4(x - 3).

💡 Strategic Tip: The signs inside the parentheses are always opposite to the point's coordinates. (+3,−2)→(x−3,y+2)(+3, -2) \rightarrow (x-3, y+2).

Choice B is incorrect because it swaps signs. Choice C is incorrect because it has the wrong x-sign. Choice D is incorrect because it swaps x and y coordinates.

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Linear Functions Set 86