Slope Calculator
Slope
The slope is a measure of the steepness of a line. It indicates how much a line rises or falls relative to its horizontal distance.
Formula
The slope \(m\) of a line passing through two points \(x_{1},y_{1}\) and \(x_{2},y_{2}\) can be calculated using the formula:
$$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$
Key Points About Slope
Positive Slope
- A positive slope indicates that the line rises as the value of \(x\)increases. The steeper the line, the greater the positive slope.
Negative Slope
- A negative slope indicates that the line falls as the value of \(x\) increases. The steeper the line, the more negative the slope.
Zero Slope
- A zero slope \((m=0)\) signifies a horizontal line, where the \(y\)-values remain constant for different \(x\)-values.
Undefined Slope
- An undefined slope occurs when the line is vertical. In this case, the denominator in the slope formula \(x_{2}-x_{1}\) becomes zero, making the fraction undefined.
Interpreting Slope Graphically
Steepness
A steeper slope corresponds to a faster rate of change.
Direction
Positive and negative slopes indicate the direction of the line.
Parallel Lines
Lines with the same slope are parallel, while lines with negative reciprocal slopes are perpendicular.
