How do you find the rate of change from the equation y = 5x + 1?

In the context of a linear equation such as y = 5x + 1, the rate of change refers to how much the value of y changes for a unit change in x. For this equation, it is in the form of y = mx + b, where m represents the slope of the line and b is the y-intercept.

In this case, the slope, which is 5, indicates that for every 1 unit increase in x, y increases by 5 units. This is the definition of the rate of change; it quantifies how one variable responds to changes in another variable—in this case, the relationship between x and y. Thus, identifying the slope of the line as the rate of change provides a clear and direct understanding of the relationship represented by the equation.

The other choices do not describe the rate of change accurately. The y-intercept refers to the point where the line crosses the y-axis, but does not indicate how y changes with respect to x. The rate of growth could be a more general term but does not specifically describe the slope in this context. The area under the curve is a concept more relevant to integral calculus and does not apply to finding the rate of change in a linear equation