Final answer:
In the slope-intercept form of a linear equation, the coefficient of x represents the slope, describing the line's steepness, while the constant term is the y-intercept, identifying where the line crosses the y-axis.
Step-by-step explanation:
In the slope-intercept form of a linear equation, which is typically written as y = mx + b or y = a + bx, the numbers represent specific characteristics of the line on a graph. The slope, often designated as m or b, measures the steepness of the line, describing how much the line rises or falls for each unit of horizontal movement. The other number, the y-intercept, represented by b or a, indicates the exact point where the line crosses the y-axis.
This means that when x = 0, the y-coordinate of the point where the line intersects the y-axis is equal to the y-intercept. For example, if an equation is y = 3x + 9, the slope (m) is 3, indicating a rise of 3 units vertically for each 1 unit of horizontal movement (rise over run), while the y-intercept (b) is 9, meaning the line crosses the y-axis at the point (0, 9).