The general equation for the slope-intercept form of a line is y = mx + b.
Here's a breakdown of what each variable represents:
- y: Represents the y-coordinate of a point on the line.
- m: Represents the slope of the line. The slope indicates the steepness and direction of the line. It is often referred to as "rise over run," meaning the change in y (vertical change) divided by the change in x (horizontal change).
- x: Represents the x-coordinate of a point on the line.
- b: Represents the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis (where x = 0). Therefore, the coordinates of the y-intercept are (0, b).
Why is this form useful?
The slope-intercept form is incredibly useful because it allows you to quickly identify two key characteristics of a line: its slope and its y-intercept. Knowing these two pieces of information makes it very easy to graph the line or to write the equation of the line if you are given the slope and y-intercept.
Example:
Consider the equation y = 2x + 3.
- The slope, m, is 2. This means for every 1 unit you move to the right on the graph (change in x), you move up 2 units (change in y).
- The y-intercept, b, is 3. This means the line crosses the y-axis at the point (0, 3).
Knowing this, you can easily plot the point (0, 3) and then use the slope to find another point on the line (e.g., move 1 unit to the right and 2 units up from (0, 3) to find the point (1, 5)). Then, draw a line through these two points to graph the entire line.
