The equation y=2.5x represents a linear relationship between the variables x and y. In this equation, 2.5 is the slope, indicating the rate at which y changes with respect to x.
The graph of this equation is a straight line that passes through the origin (0,0) since there is no constant term.
The slope of 2.5 means that for every unit increase in x, y will increase by 2.5 units. Similarly, for every unit decrease in
x, y will decrease by 2.5 units. The line rises as x increases and falls as x decreases, forming a diagonal line through the coordinate plane.
This linear relationship is characterized by its simplicity and consistency. It's a direct proportionality where the ratio of y to x remains constant, emphasizing a steady and predictable change. The steeper the slope, the greater the rate of change, and in this case, the slope of 2.5 indicates a moderately steep incline.
Understanding and graphing linear equations like y=2.5x are fundamental in mathematics and have various applications in real-world scenarios, such as representing proportional relationships in physics, economics, and other scientific fields. Overall, the graph visually illustrates the linear dependency between x and y with a constant slope of 2.5.