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

Question

BlackTom AI · Accepted Answer

For a line in standard form Ax + By = C the gradient (slope) equals -A/B, so apply that rule here.

Relevant concepts:
- Gradient (slope) of a straight line is the coefficient m in the slope-intercept form y = mx + b.
- Converting Ax + By = C to y = mx + b gives m = -A/B.
- Gradient indicates rise/run; a negative gradient means the function decreases as x increases.

Step-by-step algebra (complete reasoning and intermediate steps):
1. Start with the equation: 4x + 2y = 1.
2. Isolate y by subtracting 4x from both sides: 2y = 1 - 4x.
3. Divide every term by 2 to solve for y: y = (1/2) - (4/2)x.
4. Simplify the coefficient of x: y = 1/2 - 2x.
5. Rewrite to standard slope-intercept order: y = -2x + 1/2.

From y = -2x + 1/2, the gradient (slope) m is the coefficient of x, which is -2. Using the quick rule -A/B on the original form also yields -4/2 = -2.

Why this answer is correct:
- The coefficient of x in slope-intercept form directly gives the gradient; after rearranging we obtained -2. The alternative formula for Ax + By = C corroborates this.

Why the other options are incorrect:
- B (2): This is the absolute value of the correct slope but has the wrong sign; the line is decreasing, so the slope is negative.
- C (4): This is the coefficient of x before rearrangement but not the slope; you must divide by B (and include the negative sign).
- D (1): This is neither slope nor the y-intercept (the y-intercept is 1/2), so it is incorrect.

Conclusion: The gradient is -2, matching choice A.

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

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