3

Set 13: Linear Functions

Explanation

Answer: A

Find the slope of the line shown in the graph passing through (0,2)(0, 2) and (3,0)(3, 0).

A.

23-\frac{2}{3}

✓ Correct
B.

32-\frac{3}{2}

C.

23\frac{2}{3}

D.

32\frac{3}{2}

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Calculate rise over run from the graph. 1. Points: (0,2)(0, 2) and (3,0)(3, 0). 2. Rise: From y=2y=2 down to y=0y=0 is a change of 2-2. 3. Run: From x=0x=0 right to x=3x=3 is a change of +3+3. 4. Slope: RiseRun=23=23\frac{\text{Rise}}{\text{Run}} = \frac{-2}{3} = -\frac{2}{3}. Strategic Tip: If the line goes down from left to right, the slope MUST be negative. Choice B is incorrect because it flips rise and run. Choice C is incorrect because it misses the negative sign. Choice D is incorrect because it flips rise/run and misses the sign.

Key Steps:

The correct answer is 23-\frac{2}{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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