Final answer:
In the slope-intercept form y = mx + b, m represents the slope, determining the line's steepness, and b is the y-intercept where the line crosses the y-axis. The domain and range of a linear equation are all real numbers. The standard form of the line is achieved by rearranging the equation to Ax + By = C.
Step-by-step explanation:
Understanding the various aspects of a linear equation is fundamental in algebra. To interpret the equation of a line, we look at its slope and y-intercept. In the equation y = mx + b, m represents the slope, and b stands for the y-intercept. The line's slope determines its steepness, with a greater absolute value indicating a steeper line.
The y-intercept is the point where the line crosses the y-axis, indicated by the ordered pair (0, b).
The domain of a linear equation is all real numbers, as a line extends infinitely in both directions along the x-axis. Similarly, the range is also all real numbers because a line's y-values have no bounds.
The y-intercept is the b value in the slope-intercept form. The x-intercept can be found by setting y to zero and solving for x. The slope, expressed as a reduced fraction, represents the ratio of the rise over run, showing how much y changes with a unit change in x.
The equation of a line in slope-intercept form is y = mx + b, which is straightforward for plotting and understanding the line's behavior.
When we rearrange this equation to form Ax + By = C, we have what is known as the standard form of a linear equation. To manipulate a line, one can change the values of m or b to alter the slope and vertical position, respectively.