what are the answers to graphs of proportional relationships practice(2,14), (28,4), (42,6), (56,8),(70,10), (84, 12)
To determine if these points represent a proportional relationship, we need to check if the ratio of y-values to x-values is the same for each point.
Let's calculate the ratios for each set of points:
- For (2,14), the ratio is 14/2 = 7.
- For (28,4), the ratio is 4/28 = 1/7.
- For (42,6), the ratio is 6/42 = 1/7.
- For (56,8), the ratio is 8/56 = 1/7.
- For (70,10), the ratio is 10/70 = 1/7.
- For (84,12), the ratio is 12/84 = 1/7.
Since the ratio is consistent (1/7) for each set of points, we can conclude that these points represent a proportional relationship.
To find the answers to the graphs of proportional relationships practice, you need to determine if the given points are proportional. A proportional relationship means that there is a constant ratio between the x-values and y-values.
Let's calculate the ratios for each pair of points:
1. (2, 14): The ratio is 14/2 = 7.
2. (28, 4): The ratio is 4/28 = 1/7.
3. (42, 6): The ratio is 6/42 = 1/7.
4. (56, 8): The ratio is 8/56 = 1/7.
5. (70, 10): The ratio is 10/70 = 1/7.
6. (84, 12): The ratio is 12/84 = 1/7.
Since all the ratios are equal to 1/7, we can conclude that the given points are indeed proportional.
Therefore, the answer is: The graphs of the given points represent a proportional relationship with a constant ratio of 1/7.
To find the answers for the graphs of proportional relationships, we need to determine the constant rate of change, also known as the slope.
Step 1: Determine the rate of change (slope)
To find the rate of change, we calculate the difference in y-coordinates (vertical change) divided by the difference in x-coordinates (horizontal change) for any two points on the graph.
Using the given points (2,14) and (28,4), we can calculate the slope:
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (4 - 14) / (28 - 2) = -10 / 26 = -5 / 13
Step 2: Use the slope to find the missing values
Since we have the slope, we can use it to find the missing values in the proportional relationship.
The general form of the equation is: y = mx + b, where m represents the slope.
Given the slope of -5/13, we can use it to find the missing values.
For the x-value 42, we can calculate the corresponding y-value:
y = (-5/13) * 42 + b
To find the y-intercept (b), we can use any point on the graph. Let's use (2, 14):
14 = (-5/13) * 2 + b
14 = -10/13 + b
b = 14 + 10/13 = 14 10/13
Now, substituting the value of b back into the equation:
y = (-5/13) * 42 + 14 10/13
y = -210/13 + 186/13
y = -24/13
Therefore, the corresponding y-value for x = 42 is -24/13.
Using the same process, we can find the missing values for x = 56, x = 70, and x = 84.
For x = 56:
y = (-5/13) * 56 + 14 10/13
y = -280/13 + 186/13
y = -94/13
For x = 70:
y = (-5/13) * 70 + 14 10/13
y = -350/13 + 186/13
y = -164/13
For x = 84:
y = (-5/13) * 84 + 14 10/13
y = -420/13 + 186/13
y = -234/13
So, the corresponding y-values for x = 56, x = 70, and x = 84 are -94/13, -164/13, and -234/13, respectively.