Consider the graph shown.
A graph is shown in the xy-plane. The values on the x-axis ranges from 0 to 1 decimal point 5 in increments of 0 decimal point 5 and the values on the y-axis ranges from 0 to 800 in increments of 200. A line starts from a point 100 on the y-axis, goes up, and passes through the points (0, 100), (0 decimal point 3, 200), (0 decimal point 9, 400), and (1 decimal point 5, 600).
Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality. Explain your reasoning.
for the love of everything good and pure in the world help me
impatient much?
for the love of everything good and pure, stop with the "decimal point" crap and just type 0.3 and 0.9 !
If the line does not go through (0,0) then y and x are not proportional.
To determine if the graph shows two quantities that vary directly, we need to look at the relationship between the x-values and the y-values. In a direct variation, as the x-value increases, the y-value also increases by a constant amount.
In this graph, we can see that as the x-values increase, the y-values also increase. However, just by looking at the graph, it is not clear if the variation is direct or not.
To determine the constant of proportionality, we can calculate the ratio of the change in the y-values to the change in the x-values between two points on the graph.
Let's consider the points (0, 100) and (0.3, 200):
Change in y-values = 200 - 100 = 100
Change in x-values = 0.3 - 0 = 0.3
Now, let's consider the points (0.9, 400) and (1.5, 600):
Change in y-values = 600 - 400 = 200
Change in x-values = 1.5 - 0.9 = 0.6
To determine if the constant of proportionality is the same between these two pairs of points, we can calculate the ratios:
Ratio for (0, 100) and (0.3, 200) = Change in y-values / Change in x-values = 100 / 0.3 = 333.33
Ratio for (0.9, 400) and (1.5, 600) = Change in y-values / Change in x-values = 200 / 0.6 = 333.33
Since the ratios are the same (approximately 333.33), we can conclude that the graph shows two quantities that vary directly. The constant of proportionality is approximately 333.33.