For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
X 52 = 32 = 20 = 8
Y 39 = 24 = 15 = 6
If y varies directly with x, then y/x = k and remains constant.
6/8 = 3/4
How about the other pairs?
They all equal 3/4 cool thanks
To determine if y varies directly with x, we need to check if the ratio between y and x remains constant. Let's calculate the ratios for each pair of values:
For the first pair (x = 52, y = 39), the ratio is 39/52 ≈ 0.75.
For the second pair (x = 32, y = 24), the ratio is 24/32 = 0.75.
For the third pair (x = 20, y = 15), the ratio is 15/20 = 0.75.
For the fourth pair (x = 8, y = 6), the ratio is 6/8 = 0.75.
Since the ratio of y/x remains constant at 0.75 for all pairs, y does indeed vary directly with x.
To write the equation for direct variation, we can use the general form y = kx, where k is the constant of variation. To find k, we can choose any pair of values:
Let's use the first pair (x = 52, y = 39), and substitute the values into the equation y = kx:
39 = k * 52
To solve for k:
k = 39/52 ≈ 0.75
So, the equation for the direct variation is y ≈ 0.75x.
To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all values in the table.
Let's find the ratio of y to x for each data point:
For the first data point (52, 39), the ratio of y to x is 39/52 = 0.75.
For the second data point (32, 24), the ratio of y to x is 24/32 = 0.75.
For the third data point (20, 15), the ratio of y to x is 15/20 = 0.75.
For the fourth data point (8, 6), the ratio of y to x is 6/8 = 0.75.
Since the ratio of y to x is the same (0.75) for all data points, y does vary directly with x.
To write an equation for the direct variation, we can use the general form of a direct variation equation: y = kx, where k is the constant of variation.
We can find the value of k by using any data point in the table. Let's use the first data point (52, 39):
39 = k * 52
Solving for k:
k = 39/52
k = 0.75
Therefore, the equation for the direct variation is:
y = 0.75x