What is the average slope/rate of change between (0, 1) and (2, 4)?
What is the average slope/rate of change between (-2, 1/4) and (-1, 1/2)?
Is the slope/rate of change constant (not changing/the same)?
Is the function linear?
To find the average slope/rate of change between two points, we use the formula:
Average slope = (change in y)/(change in x)
For the points (0, 1) and (2, 4):
Change in x = 2 - 0 = 2
Change in y = 4 - 1 = 3
Average slope = 3/2 = 1.5
For the points (-2, 1/4) and (-1, 1/2):
Change in x = -1 - (-2) = 1
Change in y = 1/2 - 1/4 = 1/4
Average slope = (1/4)/1 = 1/4
The average slope between (0, 1) and (2, 4) is 1.5, and between (-2, 1/4) and (-1, 1/2) is 1/4.
To determine if the slope/rate of change is constant, we compare the slopes between different pairs of points.
The slopes 1.5 and 1/4 are different, so the slope/rate of change is not constant.
To determine if the function is linear, we check if the graph of the function would be a straight line. If the average slopes between any two points on the function are constant, then the function is linear.
Since the average slopes are not constant, the function is not linear.
To find the average slope/rate of change between two points, you can use the slope formula:
Average slope = (change in y) / (change in x)
For the first question, the two points are (0, 1) and (2, 4).
To find the change in y, subtract the y-coordinate of the first point from the y-coordinate of the second point:
Change in y = 4 - 1 = 3.
To find the change in x, subtract the x-coordinate of the first point from the x-coordinate of the second point:
Change in x = 2 - 0 = 2.
Now, divide the change in y by the change in x to get the average slope:
Average slope = 3 / 2 = 1.5.
So, the average slope/rate of change between (0, 1) and (2, 4) is 1.5.
For the second question, the two points are (-2, 1/4) and (-1, 1/2).
Change in y = (1/2) - (1/4) = 1/4.
Change in x = (-1) - (-2) = 1.
Average slope = (1/4) / 1 = 1/4.
So, the average slope/rate of change between (-2, 1/4) and (-1, 1/2) is 1/4.
If the average slope/rate of change is the same between any two points on a function, it means the slope/rate of change is constant.
To determine whether the function is linear, you need to check if a straight line can represent the relationship between the variables. In other words, if the average slope/rate of change is the same between any two points, then the function is linear. If the average slope/rate of change varies between different points, then the function is not linear. From the given information, you can determine if the average slope/rate of change is constant or not, and if it is, then the function is linear.
For the first set of points (0, 1) and (2, 4), the slope/rate of change is (4 - 1)/(2 - 0) = 3/2.
For the second set of points (-2, 1/4) and (-1, 1/2), the slope/rate of change is (1/2 - 1/4)/(-1 - (-2)) = 1/12.
The slope/rate of change is not constant between the two sets of points as they have different values.
We cannot determine whether the function is linear based on the given information.