Use the equation from Part A to predict the circumference of the tree.
C
c
Plot the new information on the same coordinate plane that you used in Part A.
A
a
(y-2)=2(x-1)
B
b
20 in.
C
c
See solution.
Practice makes perfect
a
The given table shows the circumference of a tree over the next four years.
Tree Growth
Time (yr)
1
2
3
4
Circumference (in.)
2
4
6
8
Let's discuss whether the given data is linear. One way to show that the data is linear is to plot it on a coordinate plane. In our case, let the x-axis represent time and the y-axis represent circumference. Next, we will connect the points in order to see whether they are on the same line.
As we can see, all points lie on the same line. Therefore, we can say that data is linear. Now, let's write an equation in point-slope form. First, we should determine the slope of the line by using Slope Formula. To do so, let's use the points (1,2) and (2,4).
The slope of our line is 2. Now, we are able to write the equation using one of the points on the line. Let's use the point (1,2).
(y-2)=2(x-1)
b
What do you think will happen to the circumference of the tree after 10 years? Since x represents time, we can find the circumference of the tree by substituting 10 for x into the equation that we found in Part A.
We are expecting the circumference of the tree to be 20 inches after 10 years.
c
In this part, we have been told that the actual circumference of the tree after 10 years was 43 inches, and after 4 more years it was 49 inches. Let's plot this new data on the same coordinate plane as the points used in Part A.
Now, let's connect these points to determine whether the relationship between the circumference and time is still linear.
We can see that the points do not lie on the same line anymore. Therefore, the relationship is not linear anymore.
