If you are give the relationship and you plotted vs which of the following would be true about your graph?

Question

If you are give the relationship  and you plotted  vs  which of the following would be true about your graph?

BlackTom AI · Accepted Answer

Write the given relation in straight-line form y = mx + b. If the relationship is y = (k/q^2) x + C, it already matches the linear form y = m x + b, so the slope (gradient) m and y-intercept b follow directly.

1) Relevant concepts:
- A linear equation in the form y = m x + b has gradient m and y-intercept b.
- Algebraic rearrangement can be used to put any linear relation into this form to read off slope and intercept.

2) Step-by-step reasoning:
- Start with the relation y = k x / q^2 + C.
- Group terms as y = (k / q^2) x + C.
- Compare with y = m x + b: m = k / q^2 and b = C.

3) Intermediate “calculation” steps (explicit):
- k x / q^2 is the same as (k/q^2) · x, so the coefficient of x is k/q^2.
- The remaining constant term is C, which is the value of y when x = 0.

4) Why the correct answer is correct:
- The gradient equals the coefficient multiplying the independent variable x. Here that coefficient is k/q^2, so the gradient is k/q^2.
- The y-intercept is the constant term (value of y at x = 0), which is C.

5) Why other plausible options are incorrect:
- Gradient = k (without dividing by q^2) ignores the factor q^2 in the denominator and therefore overestimates the slope.
- Gradient = k q^2 multiplies instead of dividing by q^2, which is algebraically wrong.
- y-intercept = 0 or C/q^2 are wrong because the constant term in the expression is C; it does not vanish or get divided by q^2.

Conclusion: The slope (gradient) is k/q^2 and the y-intercept is C, which matches the provided answer.

If you are give the relationship and you plotted vs which of the following would be true about your graph?单项选择题

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