In the equation y = mx + c, what does the 'm' represent?

In the equation y = mx + c, 'm' represents the slope or gradient of the line. The slope indicates how steep the line is and the direction it moves. Specifically, it describes how much y changes for a unit increase in x. If the slope is positive, the line rises as it moves from left to right, whereas a negative slope indicates that the line falls.

Understanding the meaning of the slope is crucial in linear relationships, as it allows us to determine the rate of change between the two variables represented by x and y. The value of 'm' is essential for graphing the line, as it helps to establish the angle of inclination relative to the x-axis.

The other components of the equation further clarify the relationship but do not define 'm'. The constant term, represented by 'c', corresponds to the y-intercept, which is the value of y when x is zero. This distinction helps in understanding the positioning of the line on the coordinate plane, yet it does not describe the slope itself.