(0,8), (10,15), (20,17), (30,23), (50, 31)
Y = diameter (in.)
X = time (yr)
graph name = Fir Tree Growth
a. Using the graph, describe the key characteristics of the graph (positive/negative slope, proportional/non proportional, y-intercept).
b. Write in words what the slope of the graph means in context.
c. Write in words what the y-intercept of the graph means in context.
d. Write in words what the graph of the line is showing.
a. The graph has a positive slope, indicating that as time increases, the diameter of the fir tree also increases. The graph appears to be proportional, as the increase in diameter is relatively constant over time. The y-intercept of the graph is not explicitly given in the data.
b. The slope of the graph represents the rate at which the diameter of the fir tree is increasing per year. It shows that for every year that passes, the diameter of the tree increases by a certain amount.
c. Without the y-intercept explicitly given in the data, it is difficult to determine its meaning in context. However, if the y-intercept were to represent the diameter of the fir tree at time zero, it would indicate the initial size of the tree.
d. The graph of the line is showing the growth pattern of a fir tree over time. It demonstrates that as time progresses, the diameter of the tree increases.
a. The key characteristics of the graph are:
- The slope of the graph appears to be positive.
- The graph seems to show a non-proportional relationship between time (X) and diameter (Y) of the fir tree growth.
- The y-intercept of the graph is not apparent from the given coordinate points.
b. The slope of the graph represents the rate of change, indicating how the diameter of the fir tree is changing with respect to time. In other words, it shows the average increase in diameter per unit of time.
c. Since the y-intercept is not given, it is not possible to determine its meaning in the context of the graph. The y-intercept would signify the initial diameter of the fir tree at the start of the time period, but without its value, we cannot provide a specific interpretation.
d. The graph of the line represents the growth pattern of a fir tree over time. It shows how the diameter of the tree increases with the passage of time.
a. To analyze the key characteristics of the graph, we can observe the given data points and exercise some visual inspection.
Positive/Negative Slope: By connecting the points on the graph, we can see that the line is ascending from left to right, indicating a positive slope.
Proportional/Non-proportional: To determine if the graph represents a proportional relationship, we need to examine the rate at which the y-values (diameters) change with respect to the x-values (time). If the change in y is constant as x increases, it is a proportional relationship. Conversely, if the change in y is not constant, it is a non-proportional relationship. By observing the graph, we can see that the diameter of the tree is increasing at a variable rate, suggesting a non-proportional relationship.
Y-intercept: The y-intercept represents the value of y when x is equal to zero. By moving along the x-axis until we reach the point where the line intersects it, we can determine the y-intercept. However, in this case, since we have data points starting from x = 0, we can see that the y-intercept is the value of y at the first data point, which is (0, 8).
b. The slope of the graph represents the rate of change of the y-values (diameters) with respect to the x-values (time). In the context of fir tree growth, the slope indicates how much the diameter of the tree increases for each additional year.
c. The y-intercept of the graph represents the initial diameter of the fir tree when time (x) is at zero. In this case, the y-intercept is 8, which means that at the beginning (year zero), the diameter of the fir tree was 8 inches.
d. The graph of the line is showing the relationship between time (x) and the diameter (y) of the fir tree. It illustrates how the diameter of the tree changes over time, with the x-axis representing years and the y-axis representing the corresponding diameters in inches. It provides a visual representation of the growth pattern of the fir tree.