For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.
x -4 1 10
y 18 -4.5 -45
Write an equation for the direct variation. Select the correct choice and fill in any answer boxes in your choice below.
A. y = [ ] (Use integers or decimals for any numbers in the expression.)
B. There is no direct variation.
To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all values of x and y.
First, let's calculate the ratio for the given values of x and y:
For x = -4, y = 18:
y/x = 18/(-4) = -4.5
For x = 1, y = -4.5:
y/x = -4.5/1 = -4.5
For x = 10, y = -45:
y/x = -45/10 = -4.5
The ratio y/x is constant for all values of x and y, which indicates that y varies directly with x.
To find the equation, we can write it in the form y = kx, where k is the constant of variation.
From the given ratios, we can see that k = -4.5.
Therefore, the equation for the direct variation is:
A. y = -4.5x
Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
x 36 72 76
y 9 18 19
Does y vary directly with x?
No
Yes
To determine whether y varies directly with x, we need to check if the ratio of y to x is constant for all values of x and y.
Let's calculate the ratio for the given values of x and y:
For x = 36, y = 9:
y/x = 9/36 = 0.25
For x = 72, y = 18:
y/x = 18/72 = 0.25
For x = 76, y = 19:
y/x = 19/76 = 0.25
The ratio y/x is constant for all values of x and y, which indicates that y varies directly with x.
Now let's find the constant of variation. Since the ratio y/x is constant and equal to 0.25, the constant of variation is 0.25.
The function rule for the direct variation is:
y = 0.25x
are you sure that's the constant of variation?
Apologies for the incorrect response. You are right; the constant of variation is not 0.25. Thank you for pointing that out.
To find the constant of variation, we need to calculate the ratio of y to x for each pair of values and check if it remains constant.
For x = 36, y = 9:
y/x = 9/36 = 0.25
For x = 72, y = 18:
y/x = 18/72 = 0.25
For x = 76, y = 19:
y/x = 19/76 = 0.25
The ratio y/x is indeed constant for all values of x and y. Therefore, y varies directly with x.
The constant of variation is correctly determined to be 0.25.
The function rule for the direct variation is:
y = 0.25x
Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
x 26 28 38
y 13 14 19
To determine whether y varies directly with x, we need to check if the ratio of y to x is constant for all values of x and y.
Let's calculate the ratio for the given values of x and y:
For x = 26, y = 13:
y/x = 13/26 = 0.5
For x = 28, y = 14:
y/x = 14/28 = 0.5
For x = 38, y = 19:
y/x = 19/38 = 0.5
The ratio y/x is constant for all values of x and y, which indicates that y varies directly with x.
Now let's find the constant of variation. Since the ratio y/x is constant and equal to 0.5, the constant of variation is 0.5.
The function rule for the direct variation is:
y = 0.5x
What is the constant of variation? Select the correct choice and fill in any answer boxes in your choice below.
A.
k = [ ] (Simplify your answer. Type an integer or a fraction.)
The constant of variation, k, is the coefficient that relates y and x in the direct variation equation.
From the given values, let's calculate the ratio of y to x:
For x = 26, y = 13:
y/x = 13/26 = 1/2
For x = 28, y = 14:
y/x = 14/28 = 1/2
For x = 38, y = 19:
y/x = 19/38 = 1/2
The ratio y/x is constant for all values of x and y, and it equals 1/2. Therefore, the constant of variation is k = 1/2.
What is the function rule? Select the correct choice and fill in any answer boxes in your choice below.
y = [ ]