9

Set 9: Linear Functions

Explanation

Answer: A

Which equation represents a line with slope 23\frac{2}{3} passing through (−3,−1)(-3, -1)?

A.

y+1=23(x+3)y + 1 = \frac{2}{3}(x + 3)

✓ Correct
B.

y−1=23(x−3)y - 1 = \frac{2}{3}(x - 3)

C.

y+1=23(x−3)y + 1 = \frac{2}{3}(x - 3)

D.

y−1=23(x+3)y - 1 = \frac{2}{3}(x + 3)

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Point-slope form. 1. Formula: y−y1=m(x−x1)y - y_1 = m(x - x_1). 2. Substitute: y−(−1)=23(x−(−3))y - (-1) = \frac{2}{3}(x - (-3)). 3. Simplify: y+1=23(x+3)y + 1 = \frac{2}{3}(x + 3). Strategic Tip: Signs are opposite to coordinates. Choice B is incorrect because signs are wrong. Choice C is incorrect because x-sign is wrong. Choice D is incorrect because y-sign is wrong.

Key Steps:

•

The correct answer is y+1=23(x+3)y + 1 = \frac{2}{3}(x + 3)

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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