What would you like to understand?

The final equation of the secant line intersecting the curve $y = x^2 - 4$ at $x = -1$ and $x = 2$ is $y = x - 2$. This result is derived by calculating the slope $m = 1$ between the points $(-1, -3)$ and $(2, 0)$, then applying the point-slope formula and simplifying to slope-intercept form.

Conditions: The curve is $y = x^2 - 4$.; The secant line intersects the curve at $x = -1$ and $x = 2$.; The equation is expressed in slope-intercept form ($y = mx + b$).

The final equation of the secant line intersecting the curve $y = x^2 - 4$ at $x = -1$ and $x = 2$ is $y = x - 2$. This result is derived by calculating the slope $m = 1$ between the points $(-1, -3)$ and $(2, 0)$, then applying the point-slope formula and simplifying to slope-intercept form.

Conditions: The curve is $y = x^2 - 4$.; The secant line intersects the curve at $x = -1$ and $x = 2$.; The equation is expressed in slope-intercept form ($y = mx + b$).

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 $(x_2, y_2)$.

After determining the slope $m$, substitute it and the coordinates of a known point $(x_1, y_1)$ on the line into the point-slope formula $y - y_1 = m(x - x_1)$. The resulting equation is then algebraically simplified by distributing the slope and isolating $y$ to convert it into slope-intercept form $y = mx + b$.

Conditions: The slope $m$ of the line is already known.; At least one point $(x_1, y_1)$ that lies on the line is known.; The goal is to find the equation of the line.

After determining the slope $m$, substitute it and the coordinates of a known point $(x_1, y_1)$ on the line into the point-slope formula $y - y_1 = m(x - x_1)$. The resulting equation is then algebraically simplified by distributing the slope and isolating $y$ to convert it into slope-intercept form $y = mx + b$.

Conditions: The slope $m$ of the line is already known.; At least one point $(x_1, y_1)$ that lies on the line is known.; The goal is to find the equation of the line.