I am having trouble please help me!
This chart shows the height of a tomato plant in inches, h, at weeks of growth, w.
Weeks of growth, w 4 6 10
Inches of height, h 6 9 15
Determine whether h is directly proportional to w and if so, determine the constant of proportionality.
A No, h is not directly proportional to w.
B Yes, h is directly proportional to w and the constant of proportionality is 3
C Yes, h is directly proportional to w and the constant of proportionality is 2/3
D Yes, h is directly proportional to w and the constant of proportionality is 3/2
h = 3/2 * w
To determine whether h is directly proportional to w, we need to check if the ratio of h to w is constant for all data points.
Let's calculate the ratios for the given data points:
Ratio for w = 4: h/w = 6/4 = 1.5
Ratio for w = 6: h/w = 9/6 = 1.5
Ratio for w = 10: h/w = 15/10 = 1.5
Since the ratio of h to w is the same for all data points, we can conclude that h is directly proportional to w.
To find the constant of proportionality, we can take any of the data points and divide h by w:
Using the data point w = 4 and h = 6: h/w = 6/4 = 1.5
Therefore, the constant of proportionality is 1.5.
The answer is:
C Yes, h is directly proportional to w and the constant of proportionality is 2/3
To determine whether h is directly proportional to w, we need to check if the ratios of h to w are always the same.
Let's find the ratios of h to w for each data point:
At 4 weeks of growth, the ratio of h to w is 6/4 = 1.5
At 6 weeks of growth, the ratio of h to w is 9/6 = 1.5
At 10 weeks of growth, the ratio of h to w is 15/10 = 1.5
Since the ratios of h to w are always the same (1.5), we can conclude that h is directly proportional to w.
Now, let's determine the constant of proportionality. We can choose any data point to calculate it.
Let's choose the first data point at 4 weeks of growth, where h = 6 and w = 4.
To find the constant of proportionality, we divide h by w:
Constant of proportionality = h / w = 6 / 4 = 1.5
Therefore, the answer is C. Yes, h is directly proportional to w and the constant of proportionality is 2/3.