Sure! Here are two examples of graphs showing proportional relationships:
Example 1: The relationship between the number of hours spent studying and the score obtained on a test. Let's assume that for every hour of studying, the score increases by 10 points.
Time Spent Studying (hours) | Test Score
0 | 0
1 | 10
2 | 20
3 | 30
4 | 40
In this case, the graph would be a straight line that goes through the origin (0,0) and rises at a constant rate of 10 points for each hour of studying.
Example 2: The relationship between the distance traveled and the time taken in a car traveling at a constant speed. Let's assume that the car travels at a rate of 50 miles per hour.
Time Taken (hours) | Distance Traveled (miles)
0 | 0
1 | 50
2 | 100
3 | 150
4 | 200
In this case, the graph would also be a straight line that goes through the origin (0,0) and has a slope of 50. This means that for every hour of travel, the car covers a distance of 50 miles.
These graphs represent proportional relationships because they show a constant rate of change, which means that for every increase in one variable, there is a corresponding increase in the other variable in a consistent manner.
Graphs of proportional relationships practice please
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Graphs of proportional relationships practice
The coordinates are (6, 30) (15, 3) and (10, 2)
The coordinates are (6, 30) (15, 3) and (10, 2)
To determine if these points represent a proportional relationship, we need to check if the ratios of the y-values to the x-values are consistent.
Let's find the ratios for each pair of points:
For (6, 30) and (15, 3):
Ratio = 30/6 = 5
For (6, 30) and (10, 2):
Ratio = 30/6 = 5
For (15, 3) and (10, 2):
Ratio = 3/15 = 0.2
If the ratios were consistent, they would all be the same. However, in this case, the ratio for the third pair of points is different from the other two. Therefore, these points do not represent a proportional relationship.
To visualize the points on a graph, plot them on a coordinate plane. Here's how it would look:
```
|
|
|
| * (6, 30)
|
|
|_____________
0 10 20 30
```
```
|
|
|
|
| * (15, 3)
|
|_____________
0 10 20 30
```
```
|
|
|
|
| * (10, 2)
|
|_____________
0 10 20 30
```
As we can see, the points are not aligned in a straight line, further confirming that they do not represent a proportional relationship.
Let's find the ratios for each pair of points:
For (6, 30) and (15, 3):
Ratio = 30/6 = 5
For (6, 30) and (10, 2):
Ratio = 30/6 = 5
For (15, 3) and (10, 2):
Ratio = 3/15 = 0.2
If the ratios were consistent, they would all be the same. However, in this case, the ratio for the third pair of points is different from the other two. Therefore, these points do not represent a proportional relationship.
To visualize the points on a graph, plot them on a coordinate plane. Here's how it would look:
```
|
|
|
| * (6, 30)
|
|
|_____________
0 10 20 30
```
```
|
|
|
|
| * (15, 3)
|
|_____________
0 10 20 30
```
```
|
|
|
|
| * (10, 2)
|
|_____________
0 10 20 30
```
As we can see, the points are not aligned in a straight line, further confirming that they do not represent a proportional relationship.
so what's the answer
Based on the given points (6, 30), (15, 3), and (10, 2), the answer is that these points do not represent a proportional relationship. The ratios of the y-values to the x-values are not consistent, indicating that the relationship between the variables is not proportional.
can you find the slope for that?
To find the slope of a line passing through two points, we can use the formula:
slope = (change in y) / (change in x)
Let's calculate the slope using the given points (6, 30) and (15, 3):
change in y = 3 - 30 = -27
change in x = 15 - 6 = 9
slope = (-27) / (9) = -3
The slope of this line is -3.
slope = (change in y) / (change in x)
Let's calculate the slope using the given points (6, 30) and (15, 3):
change in y = 3 - 30 = -27
change in x = 15 - 6 = 9
slope = (-27) / (9) = -3
The slope of this line is -3.
1 answer