1. Suppose y varies directly with x. Write a direct variation equation that relates x and y.
y= 7 1/2 when x=3
a. y= 3/2 x
b. y= 2/3 x
c. y= 5/2 x
d. y= 2/5 x
2. Suppose y varies directly with x. Write a direct variation equation that relates x and y.
y=10.4 when x=4
a. y= 3.4 x
b. y= 3.8 x
c. y= 3.2 x
d. y= 2.6 x
1. The correct answer is c. y= 5/2 x.
2. The correct answer is b. y= 3.8 x.
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To determine the direct variation equation, we need to find the constant of variation. This can be done by dividing the value of y by the corresponding value of x.
1. y= 7 1/2 when x=3
Constant of variation = y/x = (7 1/2) / 3 = 15/2 / 3 = 5/2
Therefore, the direct variation equation that relates x and y is: y = (5/2) x
Answer: c. y= 5/2 x
2. y=10.4 when x=4
Constant of variation = y/x = 10.4 / 4 = 2.6
Therefore, the direct variation equation that relates x and y is: y = 2.6 x
Answer: d. y= 2.6 x
To write a direct variation equation that relates x and y, you need to use the formula y = kx, where k is the constant of variation. The constant of variation represents the ratio between y and x.
For the first question, you are given that y = 7 1/2 when x = 3.
To find the constant of variation (k), you can substitute the given values into the equation and solve for k:
7 1/2 = k * 3
To simplify the equation, convert 7 1/2 to an improper fraction: 7 1/2 = 15/2
Substitute the values: 15/2 = k * 3
Simplify the equation by dividing both sides by 3:
15/2 ÷ 3 = k
k = 5/2
Therefore, the direct variation equation that relates x and y for the first question is y = (5/2) x.
So, the correct answer is c. y = 5/2 x.
For the second question, you are given that y = 10.4 when x = 4.
To find the constant of variation (k), you can substitute the given values into the equation and solve for k:
10.4 = k * 4
To solve for k, divide both sides of the equation by 4:
10.4 ÷ 4 = k
k = 2.6
Therefore, the direct variation equation that relates x and y for the second question is y = 2.6x.
So, the correct answer is d. y = 2.6x.
y = k x
7.5 = k (3)
k = 7.5/3 = 2.5 = 5/2 (c)
10.4 = k (4)
k = 10.4 /4 = 2.6 x