Line slope calculator
The slope calculator finds the slope of a line, parametric, normal, and slope y-intercept equation of a line given by coordinates of two points, A, and B, in a plane. The slope formula is sometimes referred to as a rise over run. Slope = rise/run. The calculator will calculate the slope by finding the ratio of the "vertical change" (Δy or dy) to the "horizontal change" (Δx or dx) between two distinct points, A and B, on a line. The slope is the quotient of rise over run. The horizontal line slope is zero, and the vertical line slope is undefined (infinity).
m=dxdy=ΔxΔy=x1−x0y1−y0
The slope of a line is a measure of its steepness or inclination, indicating how much the line rises or falls as it moves horizontally. It is a fundamental concept in algebra and geometry and is often represented by the letter m.
Key Points About Slope:
Definition: The slope is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
Positive Slope: If the line rises from left to right, the slope is positive. This indicates an increasing relationship between x and y.
Negative Slope: If the line falls from left to right, the slope is negative. This indicates a decreasing relationship between x and y.
Zero Slope: A horizontal line has a slope of 0 because there is no vertical change (rise = 0).
Undefined Slope: A vertical line has an undefined slope because there is no horizontal change (run = 0), and division by zero is undefined.
Interpretation: The slope describes the rate of change of y with respect to x. For example, in the equation of a line y=mx+b, m represents the slope, and b is the y-intercept.
Applications: Slope is used in various fields, such as physics (to calculate velocity), economics (to analyze trends), and engineering (to design structures).
Example:
If two points on a line are (2, 3) and (5,9), the slope is calculated as: m=(9-3)/(5-2)=6/3=2
This means the line rises 2 units vertically for every 1 unit it moves horizontally.
