What is the gradient of the linear function [math: 4x+2y=1] ?

Question

BlackTom AI · Accepted Answer

Rewriting the equation in slope–intercept form y = mx + b gives the slope directly.

1) Relevant knowledge points and concepts
- A linear equation in two variables can be written as ax + by = c.
- The slope (gradient) m of the line ax + by = c is m = −a/b.
- Equivalently, solve for y to get y = mx + b and read off m.

2) Step-by-step reasoning
Start from the given equation:
4x + 2y = 1

Subtract 4x from both sides:
2y = 1 − 4x

Divide every term by 2 to isolate y:
y = (1/2) − (4/2)x

3) Intermediate calculation steps
4/2 = 2, so:
y = (1/2) − 2x

Reorder to the usual y = mx + b form:
y = −2x + 1/2

4) Why the correct answer is correct
The coefficient of x in y = mx + b is the slope m. Here m = −2, so the gradient of the line is −2. This also matches the shortcut formula m = −a/b with a = 4 and b = 2: m = −4/2 = −2.

5) Why the other options are incorrect
- A (1): 1 is the constant term on the right-hand side before dividing; it is not the slope. The y-intercept is 1/2, not 1.
- B (4): 4 is the coefficient of x in the original form, not the slope; sign and division by the y-coefficient were not accounted for.
- D (2): 2 is the result of 4 divided by 2, but the slope is the negative of that value, so +2 is incorrect.

6) Conclusion confirming the final answer
Therefore the gradient is −2, which corresponds to option C.

What is the gradient of the linear function [math: 4x+2y=1] ?单项选择题

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