Set 7: Linear Functions (Intermediate)

Explanation

Answer: A

Which equation represents a line with a slope of $\frac{1}{2}$ and a y-intercept of $-4$ ?

$y = \frac{1}{2}x - 4$

✓ Correct

$y = -4x + \frac{1}{2}$

$y = 2x - 4$

$y = \frac{1}{2}x + 4$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Substitute $m$ and $b$ into $y = mx + b$ . 1. Given: $m = \frac{1}{2}$ , $b = -4$ . 2. Substitute: $y = (\frac{1}{2})x + (-4)$ . 3. Simplify: $y = \frac{1}{2}x - 4$ . Strategic Tip: Direct substitution into the slope-intercept form is the fastest way to write the equation. Choice B is incorrect because it swaps the slope and y-intercept. Choice C is incorrect because it uses the reciprocal of the slope. Choice D is incorrect because it has the wrong sign for the y-intercept.

Key Steps:

•

The correct answer is $y = \frac{1}{2}x - 4$

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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Set 7: Linear Functions (Intermediate)

Detailed Explanation

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