How do you calculate the slope of a secant line from two points?

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 $(x_2, y_2)$.

Reasoning, step by step

1. Identify the coordinates of the two points on the curve.
2. Assign one point as $(x_1, y_1)$ and the other as $(x_2, y_2)$.
3. Write down the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$.
4. Substitute the coordinate values into the formula.
5. Simplify the numerator and denominator, paying attention to signs.
6. Divide the results to find the slope $m$.

Example

The video states: "We’re going to use this familiar formula… M is equal to Y two minus Y one divided by X two minus X one." With points $(-1, -3)$ and $(2, 0)$, the calculation is $m = \frac{0 - (-3)}{2 - (-1)} = \frac{3}{3} = 1$.

Common misconceptions

• Mixing up the order of subtraction in the numerator and denominator (e.g., $y_1 - y_2$ over $x_2 - x_1$).
• Mishandling the subtraction of negative numbers, such as $0 - (-3)$.
• Thinking the slope is the change in x divided by the change in y.

Watch the explanation

Explore next

• Why does 0 - (-3) become $0 + 3$ in the slope calculation?
• How is the point-slope formula used after finding the slope?
• What is the final equation of the secant line in this example?