Answer: To compare the rates of change of the line y = -2x + 6 at the points (2, 2) and (1, 6), we need to find the slope (rate of change) of the line at each point.
The slope of a line is given by the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.
Using the points (2, 2) and (1, 6), we can find the slopes of the line at these points:
At point (2, 2):
slope = (y₂ - y₁) / (x₂ - x₁)
= (2 - 6) / (2 - 1)
= -4
So the slope of the line at point (2, 2) is -4.
At point (1, 6):
slope = (y₂ - y₁) / (x₂ - x₁)
= (6 - 2) / (1 - 2)
= 4
So the slope of the line at point (1, 6) is 4.
Since the slope at (1,6) is positive and greater than the slope at (2,2), we can conclude that the rate of change of y with respect to x is increasing as we move from point (2,2) to (1,6). In other words, the line is getting steeper as we move from right to left along the line.
Explanation: