A Line Has A Slope Of $-\frac{3}{5}$. Which Ordered Pairs Could Be Points On A Parallel Line? Select Two Options.A. $(-8, 8$\] And $(2, 2$\]B. $(-5, -1$\] And $(0, 2$\]C. $(-3, 6$\] And $(6,

$$

Introduction

When dealing with lines in mathematics, it's essential to understand the concept of parallel lines and how they relate to each other. Parallel lines are lines that lie in the same plane but never intersect, no matter how far they are extended. In this article, we will explore the concept of parallel lines and how to determine which ordered pairs could be points on a parallel line given a specific slope.

Understanding Slope

The slope of a line is a measure of how steep it is. It's calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope is denoted by the letter 'm' and is calculated using the formula:

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

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

Parallel Lines and Slope

Parallel lines have the same slope. This means that if we have two lines that are parallel, the slope of one line will be equal to the slope of the other line. In this case, we are given a line with a slope of $-\frac{3}{5}$. To find the ordered pairs that could be points on a parallel line, we need to find the slope of the given line and then use it to determine which ordered pairs have the same slope.

Option A: $(-8, 8)$ and $(2, 2)$

To determine if the ordered pairs $(-8, 8)$ and $(2, 2)$ could be points on a parallel line, we need to calculate the slope of the line passing through these two points. The slope is calculated using the formula:

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

where (x1, y1) = (-8, 8) and (x2, y2) = (2, 2).

m = (2 - 8) / (2 - (-8)) m = -6 / 10 m = -3/5

Since the slope of the line passing through the points $(-8, 8)$ and $(2, 2)$ is $-\frac{3}{5}$, which is the same as the slope of the given line, these two points could be on a parallel line.

Option B: $(-5, -1)$ and $(0, 2)$

To determine if the ordered pairs $(-5, -1)$ and $(0, 2)$ could be points on a parallel line, we need to calculate the slope of the line passing through these two points. The slope is calculated using the formula:

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

where (x1, y1) = (-5, -1) and (x2, y2) = (0, 2).

m = (2 - (-1)) / (0 - (-5)) m = 3 / 5

Since the slope of the line passing through the points $(-5, -1)$ and $(0, 2)$ is $\frac{3}{5}$, which is not the same as the slope of the given line, these two points could not be on a parallel line.

Option C: $(-3, 6)$ and $(6, 6)$

To determine if the ordered pairs $(-3, 6)$ and $(6, 6)$ could be points on a parallel line, we need to calculate the slope of the line passing through these two points. The slope is calculated using the formula:

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

where (x1, y1) = (-3, 6) and (x2, y2) = (6, 6).

m = (6 - 6) / (6 - (-3)) m = 0 / 9 m = 0

Since the slope of the line passing through the points $(-3, 6)$ and $(6, 6)$ is 0, which is not the same as the slope of the given line, these two points could not be on a parallel line.

Conclusion

In conclusion, the ordered pairs $(-8, 8)$ and $(2, 2)$ could be points on a parallel line with a slope of $-\frac{3}{5}$. This is because the slope of the line passing through these two points is the same as the slope of the given line. The other options, $(-5, -1)$ and $(0, 2)$, and $(-3, 6)$ and $(6, 6)$, could not be points on a parallel line with a slope of $-\frac{3}{5}$ because their slopes are different.

Final Answer

The final answer is: A

$$

Introduction

When dealing with lines in mathematics, it's essential to understand the concept of parallel lines and how they relate to each other. Parallel lines are lines that lie in the same plane but never intersect, no matter how far they are extended. In this article, we will explore the concept of parallel lines and how to determine which ordered pairs could be points on a parallel line given a specific slope.

Understanding Slope

The slope of a line is a measure of how steep it is. It's calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope is denoted by the letter 'm' and is calculated using the formula:

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

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

Parallel Lines and Slope

Parallel lines have the same slope. This means that if we have two lines that are parallel, the slope of one line will be equal to the slope of the other line. In this case, we are given a line with a slope of $-\frac{3}{5}$. To find the ordered pairs that could be points on a parallel line, we need to find the slope of the given line and then use it to determine which ordered pairs have the same slope.

Q&A: Understanding Parallel Lines

Q: What is the slope of a line?

A: The slope of a line is a measure of how steep it is. It's calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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

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

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

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

Q: What is the relationship between parallel lines and slope?

A: Parallel lines have the same slope. This means that if we have two lines that are parallel, the slope of one line will be equal to the slope of the other line.

Q: How do we determine if two lines are parallel?

A: To determine if two lines are parallel, we need to calculate the slope of each line and compare them. If the slopes are equal, then the lines are parallel.

Q: What is the significance of the slope in determining parallel lines?

A: The slope is crucial in determining parallel lines. If the slopes are equal, then the lines are parallel. If the slopes are different, then the lines are not parallel.

Q: Can two lines with different slopes be parallel?

A: No, two lines with different slopes cannot be parallel. Parallel lines must have the same slope.

Q: Can two lines with the same slope be parallel?

A: Yes, two lines with the same slope can be parallel. This means that if the slopes are equal, then the lines are parallel.

Conclusion

In conclusion, understanding parallel lines and their relationship with slope is essential in mathematics. By knowing the formula for calculating the slope of a line and the relationship between parallel lines and slope, we can determine which ordered pairs could be points on a parallel line given a specific slope.

Final Answer

The final answer is: A