5

Set 6: Linear Functions

Explanation

Answer: A

Calculate the slope of the line passing through the points (2,5)(2, 5) and (4,11)(4, 11).

A.

33

✓ Correct
B.

66

C.

13\frac{1}{3}

D.

22

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Use the slope formula m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}. 1. Substitute: Let (x1,y1)=(2,5)(x_1, y_1) = (2, 5) and (x2,y2)=(4,11)(x_2, y_2) = (4, 11). 2. Calculate: m=11542=62=3m = \frac{11 - 5}{4 - 2} = \frac{6}{2} = 3. Strategic Tip: Slope is "Rise over Run". The y-values go on top! Choice B is incorrect because it is just the change in y (11511 -5). Choice C is incorrect because it flips the fraction (Run over Rise). Choice D is incorrect because it divides the x-difference by 1 or makes a calculation error.

Key Steps:

The correct answer is 33

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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