The equation y = x represents a linear relationship between the variables y and x. In the context of linear equations, the general form can be expressed as y = mx + b, where m is the slope of the line and b is the y-intercept.
In the equation y = x, we can rewrite it to match the general form:
- y = 1x + 0
From this equation, we observe that:
- The coefficient of x is 1, which means the slope m is equal to 1.
- The constant term, or the y-intercept b, is 0, indicating that the line crosses the y-axis at the point (0, 0).
In summary, the slope of the line represented by the equation y = x is 1. This means that for every unit increase in x, the value of y also increases by one unit, resulting in a diagonal line that passes through the origin at a 45-degree angle relative to both axes.