Final answer:
The steepness of a line in a linear equation is determined by the slope, which is the coefficient 'm' in the slope-intercept form y = mx + b. In the given equation Y=2x+4, the slope is 2. Larger absolute values of slopes indicate steeper lines.
Step-by-step explanation:
The number that determines the steepness of a line in the equation y = mx + b is the slope (m). In your equation Y=2x+4, the slope is 2. This means that for each unit increase along the x-axis, y increases by 2 units, indicating a moderate incline. A steeper slope would have a larger number, whether positive for an upward slant or negative for a downward slant.
For example, comparing line graphs with the equations Y2 = -173.5 + 4.83x - 2(16.4) and Y3 = -173.5 + 4.83x + 2(16.4), we can see that both lines have the same slope value as the best-fit line, which is 4.83. This shows us that these lines rise by 4.83 units for every 1 unit they run along the x-axis. This interpretation of the slope helps us understand changes in the dependent variable (y) in response to the independent variable (x).
In general, the slope value tells us about the direction and steepness of a graphed line. If the slope is zero, the line is perfectly horizontal, while an undefined slope indicates a vertical line. The more positive or negative the slope is, the steeper the graphed line will be.