Final answer:
The equation of a line in slope-intercept form is y = mx + b, where 'm' is the slope (rise over run), and 'b' is the y-intercept, the point where the line crosses the y-axis. Some resources may list the equation as y = a + bx, but the concepts remain the same with 'a' as the y-intercept and 'b' as the slope. This equation helps in graphically expressing the linear relationship between variables.
Step-by-step explanation:
Writing an Equation of a Linear Line
The equation of a line in slope-intercept form is commonly expressed as y = mx + b where m represents the slope of the line and b represents the y-intercept.
The slope is a measure of the steepness of the line and is calculated as the rise over run. Conversely, the y-intercept is the point where the line crosses the y-axis, and is represented by the coordinate (0, b).
In some textbooks, you may see the equation written as y = a + bx, where a is the y-intercept and b is the slope. Regardless of the notation, remember that the coefficient of x represents the slope, and the constant term represents the y-intercept.
Expressing equations graphically is essential in mathematics, as it allows us to visualize the relationship between variables. The equation of the line defines its shape on the graph, with the slope determining its angle, and the y-intercept specifying where it starts on the y-axis.