Final answer:
To determine the rate of change of a function from its graph, calculate the slope by selecting two points and using the rise over run formula. The slope indicates the function's rate of change, and for a linear function, it is constant and denotes the growth rate per unit change in the x-axis.
Step-by-step explanation:
To examine the graph of a function and determine the rate of change, we look at the slope of the line. The slope is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. For a linear function, which is the graph of a line, this rate of change is constant, and is represented by the coefficient of the x term in the equation of the line, often written in the form y = mx + b, where m is the slope and b is the y-intercept.
When working with a graph, one way to calculate the slope is to pick two points on the line,
(e.g.,
(x1, y1), (x2, y2)), and use the formula:
Slope (m) = (y2 - y1) / (x2 - x1).
This will give you the rate of change of the function. When interpreting a growth rate, this can be seen as the percentage change in the 'y' value for each unit change in 'x'. To manipulate a line on a graph, you can change the slope to alter the steepness or change the y-intercept to move it up or down.