Answer:
To generate a linear function model using average rates of change, we need to have two points on the line. Let's suppose we have two points (x1, y1) and (x2, y2) on the line, where x2 > x1. Then the slope of the line, m, can be calculated as:m = (y2 - y1) / (x2 - x1)This represents the average rate of change of y with respect to x between the two points.Once we have the slope, we can use the point-slope form of the equation of a line to write the equation of the line:y - y1 = m(x - x1)where (x1, y1) is one of the points on the line.To simplify this equation, we can rearrange it to slope-intercept form, y = mx + b, where b is the y-intercept. We can solve for b by plugging in the coordinates of one of the points on the line:y1 = mx1 + bb = y1 - mx1Once we have m and b, we can write the equation of the line in slope-intercept form:y = mx + bHere's an example: Suppose we have the two points (2, 5) and (4, 9). The slope of the line between these two points is:m = (y2 - y1) / (x2 - x1) = (9 - 5) / (4 - 2) = 2Using point-slope form, we can write the equation of the line as:y - 5 = 2(x - 2)Simplifying, we get:y = 2x + 1So the linear function model generated using average rates of change is y = 2x + 1.
Explanation: