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To calculate the slope of a secant line, use the two-point formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ on the curve. This requires that $x_2 \neq x_1$ to avoid division by zero, ensuring the slope represents the change in y divided by the change in x.

Conditions: Two distinct points on the curve are known or have been calculated.; The x-coordinates of the two points are different ($x_2 \neq x_1$) to avoid division by zero.; The points are $(x_1, y_1)$ and $(x_2, y_2)$.

To calculate the slope of a secant line, use the two-point formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ on the curve. This requires that $x_2 \neq x_1$ to avoid division by zero, ensuring the slope represents the change in y divided by the change in x.

Conditions: Two distinct points on the curve are known or have been calculated.; The x-coordinates of the two points are different ($x_2 \neq x_1$) to avoid division by zero.; The points are $(x_1, y_1)$ and $(x_2, y_2)$.

Subtracting a negative number is mathematically equivalent to adding its positive counterpart. In the slope calculation, the expression $0 - (-3)$ represents the difference between the y-coordinates.

Conditions: The arithmetic operation involves subtracting a negative number.; The context is evaluating the numerator of the slope formula $y_2 - y_1$.; The values are $y_2 = 0$ and $y_1 = -3$.

Subtracting a negative number is mathematically equivalent to adding its positive counterpart. In the slope calculation, the expression $0 - (-3)$ represents the difference between the y-coordinates.

Conditions: The arithmetic operation involves subtracting a negative number.; The context is evaluating the numerator of the slope formula $y_2 - y_1$.; The values are $y_2 = 0$ and $y_1 = -3$.

To find the point on the curve $y = x^2 - 4$ at $x = -1$, substitute $x = -1$ into the equation. Evaluating $(-1)^2 - 4$ yields $1 - 4 = -3$, so the coordinates of the point are $(-1, -3)$.

Conditions: The curve is defined by the equation $y = x^2 - 4$.; The x-coordinate of the desired point is given as $-1$.; The point must lie on the curve.

To find the point on the curve $y = x^2 - 4$ at $x = -1$, substitute $x = -1$ into the equation. Evaluating $(-1)^2 - 4$ yields $1 - 4 = -3$, so the coordinates of the point are $(-1, -3)$.

Conditions: The curve is defined by the equation $y = x^2 - 4$.; The x-coordinate of the desired point is given as $-1$.; The point must lie on the curve.