What does the slope represent in the linear equation y = mx + b?

What does the slope represent in the linear equation y = mx + b?

• A. The rate of change.
• B. The y-intercept.
• C. The x-coordinate of the line.
• D. The constant term.

Answer: (A)

The slope measures how y changes as x changes—the rate of change of the function. In y = mx + b, for every 1 unit increase in x, y changes by m units. So the slope tells you how steep the line is and whether y goes up or down as x grows. The y-intercept b is where the line crosses the y-axis, not the slope. A line has many x-values, so there isn’t a single x-coordinate that defines it, and the constant term refers to b. If you think in terms of rise over run, m equals Δy/Δx, reinforcing that the slope is the rate of change.

The slope measures how y changes as x changes—the rate of change of the function. In y = mx + b, for every 1 unit increase in x, y changes by m units. So the slope tells you how steep the line is and whether y goes up or down as x grows. The y-intercept b is where the line crosses the y-axis, not the slope. A line has many x-values, so there isn’t a single x-coordinate that defines it, and the constant term refers to b. If you think in terms of rise over run, m equals Δy/Δx, reinforcing that the slope is the rate of change.