The equation y = 2.4x signifies growth, with a positive slope indicating that for every unit increase in x, y increases by 2.4 units. The y-intercept is at the origin (0, 0). This linear relationship illustrates a scenario where the dependent variable y grows with an increase in the independent variable x.
The given equation is y = 2.4x, where y is the dependent variable, x is the independent variable, and the coefficient 2.4 represents the slope of the line. To analyze whether this represents growth or decay and to determine the y-intercept, it's crucial to understand the form of the equation, y = mx + b, where m is the slope and b is the y-intercept.
In the given equation, the slope m is 2.4. The y-intercept (b) occurs when x = 0. Substituting x = 0 into the equation, we find that y = 0. Therefore, the y-intercept is at the origin, (0, 0).
Since the slope is positive (2.4), the line represents growth. For every unit increase in x, y increases by 2.4 units. The positive slope signifies a positive correlation between x and y, indicating a growth pattern.
In summary, the equation y = 2.4x has a y-intercept at the origin (0, 0), and the positive slope implies growth. The line describes a scenario where the dependent variable y increases with an increase in the independent variable x, reflecting a growth relationship.