I need help urgently for unit 6 lesson 10.
for the data in the table does y vary with x? If it does, write an equation for he direct variation.
X Y
10 12
15 18
20 24
a. yes; y=1.2x**
b. yes; y=2x
c. yes; y=x+1
d. no; y does not vary directly with x.
Yes, a.
To determine if y varies with x, we need to check if there is a constant ratio between y and x. Let's examine the values in the table:
When x = 10, y = 12
When x = 15, y = 18
When x = 20, y = 24
To check the ratio, we can divide y by x for each pair of values:
12 ÷ 10 = 1.2
18 ÷ 15 = 1.2
24 ÷ 20 = 1.2
Since the ratio between y and x is always 1.2, we can conclude that y varies directly with x.
Therefore, the correct answer would be: a. yes; y=1.2x.
To determine if y varies with x, we need to observe the relationship between the two variables.
In this case, we can look at the values in the table:
X Y
10 12
15 18
20 24
To check if y varies with x, we can see if there is a constant ratio between the values of y and x. If the ratio remains the same for all the data points, then we can conclude that y varies directly with x.
Let's calculate the ratios for the data points:
For the first data point (10, 12), the ratio is 12/10 = 1.2.
For the second data point (15, 18), the ratio is 18/15 = 1.2.
For the third data point (20, 24), the ratio is 24/20 = 1.2.
Since the ratio remains constant as 1.2 for all the data points, we can conclude that y varies directly with x.
Now, to write the equation for direct variation, we know that in direct variation, the equation is of the form y = kx, where k is the constant of variation.
Using any of the data points, we can substitute the values of x and y to solve for k.
Let's use the first data point (10, 12):
12 = k * 10
Now, solve for k:
k = 12/10 = 1.2
Therefore, the equation for direct variation is y = 1.2x.
So, the correct answer is option a. yes; y=1.2x.