7

Set 4: Linear Functions (Advanced)

Explanation

Answer: A

Which equation represents a line parallel to y=2x+1y = 2x + 1 passing through (0,4)(0, 4)?

A.

y=2x+4y = 2x + 4

✓ Correct
B.

y=2x+1y = 2x + 1

C.

y=12x+4y = -\frac{1}{2}x + 4

D.

y=4x+2y = 4x + 2

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Same slope, new intercept. 1. Slope: Parallel to y=2x+1y=2 x+1 means m=2m=2. 2. Intercept: Passes through (0,4)(0, 4), so b=4b=4. 3. Equation: y=2x+4y = 2 x + 4. Strategic Tip: Keep the mxmx part, change the bb part. Choice B is incorrect because it is the same line (coincident, not distinct parallel usually, though technically parallel lines can be coincident in some definitions, usually distinct is implied. If distinct required, A is best. If not, A is still correct for the point). Choice C is incorrect because perpendicular. Choice D is incorrect because swaps slope and intercept.

Key Steps:

The correct answer is y=2x+4y = 2x + 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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