Calculating Slope from Two Points
The slope formula m = (y₂ − y₁) / (x₂ − x₁) calculates the rate of change between any two points on a line, a fundamental skill in Grade 11 enVision Algebra 1 (Chapter 2: Linear Equations). Students identify (x₁, y₁) and (x₂, y₂), subtract the y-coordinates for the numerator (rise), and subtract the x-coordinates in the same order for the denominator (run). A positive slope rises left to right; a negative slope falls. Slope is essential for writing equations of lines and analyzing linear relationships.
Key Concepts
The slope between two points $(x 1, y 1)$ and $(x 2, y 2)$ is calculated using the slope formula: $$m = \frac{y 2 y 1}{x 2 x 1}$$.
Common Questions
What is the slope formula?
The slope between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ − y₁) / (x₂ − x₁), representing rise over run.
What does a positive slope indicate?
A positive slope means the line rises from left to right — as x increases, y increases.
What does a negative slope indicate?
A negative slope means the line falls from left to right — as x increases, y decreases.
What is a common error when using the slope formula?
Subtracting the coordinates in different orders: using (y₂ − y₁) in the numerator but (x₁ − x₂) in the denominator, which changes the sign of the result.
What is slope of a horizontal line?
A horizontal line has slope m = 0, because y₂ − y₁ = 0 for any two points on it.
What is the slope of a vertical line?
A vertical line has undefined slope, because x₂ − x₁ = 0, causing division by zero.