Determine the constant of proportionality (k) for the table and write the relationship between y and x.
(1 point)
Responses
k = 17
k = 1 seventh
k = −17
k = negative 1 seventh
k = -7
k = -7
k = 7
k = 7
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The correct answer is: K = 7
Not negative seven, not 17.
Determine the independent variable, X: The independent variable is the one that is not dependent on other variables. In this case, the independent variable (X) corresponds to the values 9, 4, 2, and 11.
Determine the dependent variable, Y: The dependent variable is the one that changes based on the independent variable. Here, the dependent variable (Y) corresponds to the values 63, 28, 14, and 77.
Calculate the constant of proportionality (k):
We use the formula: k = Y / X.
Let’s compute k for each pair of values:
For X = 9, Y = 63:
k = Y / X = 63 / 9 = 7.
For X = 4, Y = 28:
k = Y / X = 28 / 4 = 7.
For X = 2, Y = 14:
k = Y / X = 14 / 2 = 7.
For X = 11, Y = 77:
k = Y / X = 77 / 11 = 7.
Since the value of k remains consistent (equal to 7) for all pairs of values, we can conclude that the relationship between Y and X is directly proportional. Specifically, we can express it as:
[ Y = kX ]
where k is the constant of proportionality, which in this case is 7. 📏🔍
Remember that the constant of proportionality represents the unit rate of a linear relationship, and it’s also known as the slope or gradient when graphed. If you’d like to explore more about linear regression, feel free to check out our slope calculator and gradient calculator
To determine the constant of proportionality (k), you can calculate it by dividing any y value by its corresponding x value. For example:
y = 119 when x = 7
k = y/x
k = 119/7
k = 17
So, the correct answer is:
k = 17
The relationship between y and x is y = 17x.