The Slope-Intercept Form of a Linear Equation
The slope-intercept form of a linear equation is . Move slider . See the steepness of the line change. The slope of the line is . When is negative, the direction of the line changes. When , the line is flat. Vertical lines do not have a slope. Where the line intersects the -axis is the -intercept point of the line. The -intercept is the point . Only the is used in the equation, and it is the constant term of the equation. Move slider . See the line move up or down. When is positive, the y-intercept is above the -axis. When is negative, the y-intercept is below the -axis.
To remember the different meaning for different slope values: It is easy to walk across the flat ground. When , it is like flat ground. Some climbs are barely hills, some are challenging hikes, and others require major planning and safety gear. When , the climb is barely a hill. When , the slope is 45 degree from the -axis and is a challenging hike. When , the line approaches the -axis and becomes a major climb requiring planning and safety gear. Only dare devils would scale the side of a skyscraper. The steepness of a vertical line is akin to scaling the side of a skyscraper. The slope does not exist.