Is (6,1), (3,3), (0,5) non proportional
To determine if points (6, 1), (3, 3), and (0, 5) are non-proportional, we need to check if the ratios of the y-coordinate to the x-coordinate are different for each pair of points.
First, let's calculate the ratios for each pair of points:
For (6, 1) and (3, 3):
Ratio = (y-coordinate)/(x-coordinate) = 1/6 and 3/3 = 1
Both ratios are equal, so these points are proportional.
For (6, 1) and (0, 5):
Ratio = (y-coordinate)/(x-coordinate) = 1/6 and 5/0 (undefined)
The ratio for the second pair is undefined, so these points are not proportional.
For (3, 3) and (0, 5):
Ratio = (y-coordinate)/(x-coordinate) = 3/3 and 5/0 (undefined)
The ratio for the second pair is also undefined, so these points are not proportional.
Therefore, the points (6, 1), (3, 3), and (0, 5) are non-proportional.
To determine if the points (6, 1), (3, 3), and (0, 5) are non-proportional, we need to check if the ratios of the y-coordinates to the x-coordinates are equal for the different pairs of points.
Let's calculate the ratios of the y-coordinates to the x-coordinates for each pair of points:
For points (6, 1) and (3, 3):
- The ratio for (6, 1) is 1/6.
- The ratio for (3, 3) is 3/3 = 1.
For points (3, 3) and (0, 5):
- The ratio for (3, 3) is 3/3 = 1.
- The ratio for (0, 5) is 5/0, which is undefined because we can't divide by zero.
Since the ratio of the y-coordinates to the x-coordinates is not equal for all pairs of points, we can conclude that the points (6, 1), (3, 3), and (0, 5) are non-proportional.
To determine if the given points (6,1), (3,3), (0,5) are non-proportional, we can calculate the slopes between each pair of points and compare them.
The slope between two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slopes:
1. Slope between (6,1) and (3,3):
slope1 = (3 - 1) / (3 - 6)
= 2 / -3
= -2/3
2. Slope between (3,3) and (0,5):
slope2 = (5 - 3) / (0 - 3)
= 2 / -3
= -2/3
3. Slope between (6,1) and (0,5):
slope3 = (5 - 1) / (0 - 6)
= 4 / -6
= -2/3
Comparing the slopes, we can see that all the slopes (-2/3, -2/3, and -2/3) are equal. Thus, the given points are proportional.