The following points show how many centimeters a bamboo plant can grow (g) and the hours (h) that the plant has been growing. What is k?(g,h)
(10,50) (20,100) (50,250)
To determine the value of k in the given scenario, we need to find the relationship between the growth of the bamboo plant (g) and the hours it has been growing (h).
Looking at the given data points:
(10,50)
(20,100)
(50,250)
We can establish an equation in the form of g = kh.
Let's plug in the first data point (10,50) to find the value of k:
50 = k * 10
Dividing both sides by 10:
5 = k
Therefore, the value of k is 5 in the given scenario.
To find the value of k, we can use the formula for linear equations, which is y = mx + b, where y represents the dependent variable (in this case, the growth in centimeters), x represents the independent variable (in this case, the hours the plant has been growing), m represents the slope, and b represents the y-intercept.
Let's use the first set of points (10, 50) to find the value of the slope (m):
Using the formula, we can substitute the values:
50 = 10m + b
Now, let's use the second set of points (20, 100) to set up another equation:
100 = 20m + b
Now we have two equations:
50 = 10m + b
100 = 20m + b
To solve this system of equations, we can subtract the first equation from the second equation:
(100 - 50) = (20 - 10)m + (b - b)
Simplifying:
50 = 10m
Dividing both sides by 10:
5 = m
Now that we have the slope (m), we can substitute it back into either of the original equations to find the value of b (the y-intercept). Let's use the first equation:
50 = 10m + b
Substituting the slope:
50 = 10(5) + b
Simplifying:
50 = 50 + b
Subtracting 50 from both sides:
b = 0
So, the equation for the linear relationship between the growth in centimeters (g) and the hours (h) that the plant has been growing is:
g = 5h + 0
Therefore, the value of k is 5.