What is the final equation of the secant line in this example?

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 ($y = mx + b$).

Reasoning, step by step

1. Calculate the y-coordinates for $x = -1$ and $x = 2$ to get points $(-1, -3)$ and $(2, 0)$.
2. Compute the slope $m = \frac{0 - (-3)}{2 - (-1)} = 1$.
3. Substitute $m = 1$ and point $(-1, -3)$ into the point-slope formula: $y - (-3) = 1(x - (-1))$.
4. Simplify the equation: $y + 3 = x + 1$.
5. Subtract 3 from both sides to isolate y: $y = x - 2$.

Example

The video states: "So we have y is equal to x minus two. This is the equation of the secant line. This is the final answer." The board shows the boxed equation $y = x - 2$.

Common misconceptions

• Writing the equation in standard form ($Ax + By = C$) when slope-intercept form is expected.
• Making an arithmetic error when subtracting 3 from both sides.
• Using the wrong point in the point-slope formula, though this would still yield the same final equation if done correctly.

Watch the explanation

Explore next

• How can you verify that the line $y = x - 2$ passes through the points (-1, -3) and (2, 0)?
• What is the y-intercept of the secant line?
• How does the graph of $y = x - 2$ relate to the graph of $y = x^2 - 4$?