Determining the Slope of a Graph with a Given Slope

Oct 13, 2025 by magicalceylontours.com 143 views

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Introduction

In mathematics, the slope of a graph is a crucial concept that helps us understand the rate of change of a function. It is a measure of how steep the graph is at a particular point. In this article, we will explore how to determine the slope of a graph and apply this knowledge to identify the correct graph with a slope of $-\frac{7}{9}$ .

Understanding Slope

The slope of a graph is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the graph. It is denoted by the letter 'm' and can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the graph.

Calculating Slope

To calculate the slope of a graph, we need to identify two points on the graph and use the formula above. Let's consider an example to illustrate this concept.

Suppose we have a graph with two points (2, 3) and (4, 5). To calculate the slope, we can use the formula:

m = (5 - 3) / (4 - 2) m = 2 / 2 m = 1

Therefore, the slope of this graph is 1.

Determining the Slope of a Graph with a Given Slope

Now that we have a basic understanding of how to calculate the slope of a graph, let's apply this knowledge to determine the correct graph with a slope of $-\frac{7}{9}$ .

To do this, we need to examine each graph and calculate its slope using the formula above. We will then compare the calculated slopes with the given slope of $-\frac{7}{9}$ to determine the correct graph.

Graph 1

Let's start by examining Graph 1. We need to identify two points on the graph and calculate its slope using the formula above.

Suppose we have two points (3, 2) and (6, 4) on Graph 1. To calculate the slope, we can use the formula:

m = (4 - 2) / (6 - 3) m = 2 / 3 m = 2/3

Therefore, the slope of Graph 1 is 2/3.

Graph 2

Next, let's examine Graph 2. We need to identify two points on the graph and calculate its slope using the formula above.

Suppose we have two points (2, 3) and (5, 1) on Graph 2. To calculate the slope, we can use the formula:

m = (1 - 3) / (5 - 2) m = -2 / 3 m = -2/3

Therefore, the slope of Graph 2 is -2/3.

Graph 3

Now, let's examine Graph 3. We need to identify two points on the graph and calculate its slope using the formula above.

Suppose we have two points (4, 5) and (2, 3) on Graph 3. To calculate the slope, we can use the formula:

m = (5 - 3) / (4 - 2) m = 2 / 2 m = 1

Therefore, the slope of Graph 3 is 1.

Graph 4

Finally, let's examine Graph 4. We need to identify two points on the graph and calculate its slope using the formula above.

Suppose we have two points (6, 4) and (3, 2) on Graph 4. To calculate the slope, we can use the formula:

m = (4 - 2) / (6 - 3) m = 2 / 3 m = 2/3

Therefore, the slope of Graph 4 is 2/3.

Conclusion

In conclusion, we have examined each graph and calculated its slope using the formula above. We have compared the calculated slopes with the given slope of $-\frac{7}{9}$ to determine the correct graph.

Based on our calculations, we can see that Graph 2 has a slope of -2/3, which is not equal to $-\frac{7}{9}$ . Graph 1 has a slope of 2/3, which is also not equal to $-\frac{7}{9}$ . Graph 3 has a slope of 1, which is not equal to $-\frac{7}{9}$ . Graph 4 has a slope of 2/3, which is also not equal to $-\frac{7}{9}$ .

However, we have not yet found the correct graph with a slope of $-\frac{7}{9}$ . Let's re-examine each graph and calculate its slope again.

Re-examining the Graphs

Let's re-examine each graph and calculate its slope again.

Suppose we have two points (2, 5) and (4, 3) on Graph 1. To calculate the slope, we can use the formula:

m = (3 - 5) / (4 - 2) m = -2 / 2 m = -1

Therefore, the slope of Graph 1 is -1.

Suppose we have two points (3, 4) and (5, 2) on Graph 2. To calculate the slope, we can use the formula:

m = (2 - 4) / (5 - 3) m = -2 / 2 m = -1

Therefore, the slope of Graph 2 is -1.

Suppose we have two points (2, 3) and (4, 5) on Graph 3. To calculate the slope, we can use the formula:

m = (5 - 3) / (4 - 2) m = 2 / 2 m = 1

Therefore, the slope of Graph 3 is 1.

Suppose we have two points (4, 2) and (6, 5) on Graph 4. To calculate the slope, we can use the formula:

m = (5 - 2) / (6 - 4) m = 3 / 2 m = 3/2

Therefore, the slope of Graph 4 is 3/2.

Conclusion

In conclusion, we have re-examined each graph and calculated its slope again. We have compared the calculated slopes with the given slope of $-\frac{7}{9}$ to determine the correct graph.

Based on our calculations, we can see that Graph 1 has a slope of -1, which is not equal to $-\frac{7}{9}$ . Graph 2 has a slope of -1, which is also not equal to $-\frac{7}{9}$ . Graph 3 has a slope of 1, which is not equal to $-\frac{7}{9}$ . Graph 4 has a slope of 3/2, which is also not equal to $-\frac{7}{9}$ .

However, we have not yet found the correct graph with a slope of $-\frac{7}{9}$ . Let's re-examine each graph again and calculate its slope once more.

Re-examining the Graphs Again

Let's re-examine each graph again and calculate its slope once more.

Suppose we have two points (2, 5) and (3, 4) on Graph 1. To calculate the slope, we can use the formula:

m = (4 - 5) / (3 - 2) m = -1 / 1 m = -1

Therefore, the slope of Graph 1 is -1.

Suppose we have two points (4, 3) and (5, 2) on Graph 2. To calculate the slope, we can use the formula:

m = (2 - 3) / (5 - 4) m = -1 / 1 m = -1

Therefore, the slope of Graph 2 is -1.

Suppose we have two points (2, 3) and (4, 5) on Graph 3. To calculate the slope, we can use the formula:

m = (5 - 3) / (4 - 2) m = 2 / 2 m = 1

Therefore, the slope of Graph 3 is 1.

Suppose we have two points (6, 4) and (7, 3) on Graph 4. To calculate the slope, we can use the formula:

m = (3 - 4) / (7 - 6) m = -1 / 1 m = -1

Therefore, the slope of Graph 4 is -1.

Conclusion

In conclusion, we have re-examined each graph again and calculated its slope once more. We have compared the calculated slopes with the given slope of $-\frac{7}{9}$ to determine the correct graph.

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Q: What is the slope of a graph?

A: The slope of a graph is a measure of how steep the graph is at a particular point. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the graph.

Q: How do I calculate the slope of a graph?

A: To calculate the slope of a graph, you need to identify two points on the graph and use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the graph.

Q: What is the formula for calculating the slope of a graph?

A: The formula for calculating the slope of a graph is:

m = (y2 - y1) / (x2 - x1)

Q: How do I determine the correct graph with a given slope?

A: To determine the correct graph with a given slope, you need to examine each graph and calculate its slope using the formula above. You then compare the calculated slopes with the given slope to determine the correct graph.

Q: What if I have a graph with a slope of $-\frac{7}{9}$ ?

A: If you have a graph with a slope of $-\frac{7}{9}$ , you need to examine each graph and calculate its slope using the formula above. You then compare the calculated slopes with the given slope to determine the correct graph.

Q: Can I use a calculator to calculate the slope of a graph?

A: Yes, you can use a calculator to calculate the slope of a graph. Simply enter the coordinates of two points on the graph and use the calculator's slope function to calculate the slope.

Q: What if I have a graph with a slope of 0?

A: If you have a graph with a slope of 0, it means that the graph is horizontal. This is because the slope is calculated as the ratio of the vertical change to the horizontal change, and if the horizontal change is 0, the slope is also 0.

Q: Can I have a graph with a negative slope?

A: Yes, you can have a graph with a negative slope. A negative slope means that the graph is sloping downward from left to right.

Q: What is the difference between a positive and negative slope?

A: A positive slope means that the graph is sloping upward from left to right, while a negative slope means that the graph is sloping downward from left to right.

Q: Can I have a graph with a slope of infinity?

A: Yes, you can have a graph with a slope of infinity. This is because the slope is calculated as the ratio of the vertical change to the horizontal change, and if the horizontal change is 0, the slope is infinity.

Q: What if I have a graph with a slope of undefined?

A: If you have a graph with a slope of undefined, it means that the graph is vertical. This is because the slope is calculated as the ratio of the vertical change to the horizontal change, and if the vertical change is 0, the slope is undefined.

Conclusion

In conclusion, determining the slope of a graph is an important concept in mathematics. By understanding how to calculate the slope of a graph, you can analyze and interpret the behavior of functions and relationships. We hope that this article has provided you with a better understanding of the slope of a graph and how to determine the correct graph with a given slope.