use the table below to determine whether y varies directly with x. if it does, find the constant of variation k and write the relationship as y=kx.
x 3 5 6 8
y 7 11 13 19
To determine if y varies directly with x, we need to check if the ratio of y to x is constant across all values.
Using the values from the table, we find:
For x = 3, y = 7. Therefore, the ratio of y to x is 7/3 = 2.33.
For x = 5, y = 11. The ratio of y to x is 11/5 = 2.2.
For x = 6, y = 13. The ratio of y to x is 13/6 ≈ 2.17.
For x = 8, y = 19. The ratio of y to x is 19/8 ≈ 2.38.
Since the ratio of y to x is not constant across all values, y does not vary directly with x.
Therefore, we cannot find a constant of variation (k) or write the relationship as y = kx.
To determine if y varies directly with x, we need to check if the ratio y/x remains constant for all the data points in the table.
Let's calculate the ratio for each pair of values:
For the first pair (3, 7): 7/3 = 2.3333...
For the second pair (5, 11): 11/5 = 2.2
For the third pair (6, 13): 13/6 = 2.1666...
For the fourth pair (8, 19): 19/8 = 2.375
Since the ratios are not the same for each pair of values, y does not vary directly with x.
Therefore, we cannot find the constant of variation (k) or write the relationship as y = kx in this case.
To determine if y varies directly with x using the given table, we need to check if the ratio of y to x remains constant across all values.
Let's calculate the ratios for each pair of x and y values:
For the first pair (x=3, y=7), the ratio is 7/3 ≈ 2.33.
For the second pair (x=5, y=11), the ratio is 11/5 = 2.2.
For the third pair (x=6, y=13), the ratio is 13/6 ≈ 2.17.
For the fourth pair (x=8, y=19), the ratio is 19/8 ≈ 2.38.
Since the ratios are not exactly equal, y does not vary directly with x. However, we can calculate an approximate constant of variation (k) by taking the average of the ratios:
Average ratio = (2.33 + 2.2 + 2.17 + 2.38) / 4 ≈ 2.27.
So, the approximate constant of variation (k) is 2.27, and the relationship between y and x can be expressed as y = 2.27x.