Line { R $}$ Has A Slope Of { \frac{-5}{9}$}$. Line { S $}$ Is Parallel To Line { R $}$. What Is The Slope Of Line { S $}$?Simplify Your Answer And Write It As A Proper Fraction, Improper Fraction,
When dealing with lines in mathematics, one of the key concepts to grasp is the slope. The slope of a line is a measure of how steep it is and can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where m is the slope, and (x1, y1) and (x2, y2) are two points on the line.
In this article, we will explore the concept of slope and parallel lines, and how they relate to each other. We will also use the given information to find the slope of a line that is parallel to another line with a known slope.
The Slope of Line { r $}$
The slope of line { r $}$ is given as {\frac{-5}{9}$}$. This means that for every 9 units moved horizontally, the line moves down by 5 units.
Parallel Lines
Two lines are said to be parallel if they never intersect, no matter how far they are extended. In other words, parallel lines have the same slope but different y-intercepts.
The Slope of Line { s $}$
Since line { s $}$ is parallel to line { r $}$, it must have the same slope as line { r $}$. Therefore, the slope of line { s $}$ is also {\frac{-5}{9}$}$.
Simplifying the Slope
The slope of line { s $}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of -5 and 9 is 1, so the slope cannot be simplified further.
Improper Fraction
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In this case, the slope of line { s $}$ is already in its simplest form, so it is not an improper fraction.
Conclusion
In conclusion, the slope of line { s $}$ is {\frac{-5}{9}$}$. This means that for every 9 units moved horizontally, line { s $}$ will move down by 5 units.
Key Takeaways
- The slope of a line is a measure of how steep it is.
- Parallel lines have the same slope but different y-intercepts.
- The slope of line { s $}$ is the same as the slope of line { r $}$.
- The slope of line { s $}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor.
Frequently Asked Questions
- Q: What is the slope of line { s $}$? A: The slope of line { s $}$ is {\frac{-5}{9}$}$.
- Q: Why is the slope of line { s $}$ the same as the slope of line { r $}$? A: Because line { s $}$ is parallel to line { r $}$.
- Q: Can the slope of line { s $}$ be simplified further? A: No, the slope of line { s $}$ is already in its simplest form.
Additional Resources
For more information on slope and parallel lines, check out the following resources:
- Khan Academy: Slope and Linear Equations
- Mathway: Slope and Parallel Lines
- Wolfram Alpha: Slope and Parallel Lines
References
In our previous article, we explored the concept of slope and parallel lines. We discussed how the slope of a line is a measure of how steep it is and how parallel lines have the same slope but different y-intercepts. In this article, we will answer some frequently asked questions about slope and 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 can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where m is the slope, and (x1, y1) and (x2, y2) are two points on the line.
Q: How do you find the slope of a line?
A: To find the slope of a line, you can use the formula: m = (y2 - y1) / (x2 - x1). You can also use a graphing calculator or a online tool to find the slope of a line.
Q: What is the difference between a slope and a y-intercept?
A: The slope of a line is a measure of how steep it is, while the y-intercept is the point where the line intersects the y-axis. The slope and y-intercept are two different concepts, but they are related in that the slope determines the steepness of the line, while the y-intercept determines the point where the line intersects the y-axis.
Q: Can a line have a slope of 0?
A: Yes, a line can have a slope of 0. This means that the line is horizontal and does not change in the y-direction.
Q: Can a line have a slope of infinity?
A: No, a line cannot have a slope of infinity. A slope of infinity would mean that the line is vertical and does not change in the x-direction.
Q: What is the relationship between the slope of a line and its equation?
A: The slope of a line is related to its equation by the formula: y = mx + b, where m is the slope, x is the independent variable, and b is the y-intercept.
Q: Can a line have a negative slope?
A: Yes, a line can have a negative slope. This means that the line slopes downward from left to right.
Q: Can a line have a positive slope?
A: Yes, a line can have a positive slope. This means that the line slopes upward from left to right.
Q: What is the relationship between the slope of a line and its graph?
A: The slope of a line is related to its graph by the fact that the slope determines the steepness of the line. A line with a steep slope will have a steeper graph, while a line with a shallow slope will have a flatter graph.
Q: Can a line have a slope of 1?
A: Yes, a line can have a slope of 1. This means that the line slopes upward from left to right at a 45-degree angle.
Q: Can a line have a slope of -1?
A: Yes, a line can have a slope of -1. This means that the line slopes downward from left to right at a 45-degree angle.
Q: What is the relationship between the slope of a line and its perpendicular line?
A: The slope of a line is related to its perpendicular line by the fact that the slope of the perpendicular line is the negative reciprocal of the slope of the original line.
Q: Can a line have a slope of 0 and a perpendicular line?
A: No, a line cannot have a slope of 0 and a perpendicular line. A line with a slope of 0 is horizontal and does not have a perpendicular line.
Q: Can a line have a slope of infinity and a perpendicular line?
A: No, a line cannot have a slope of infinity and a perpendicular line. A line with a slope of infinity is vertical and does not have a perpendicular line.
Conclusion
In conclusion, the slope of a line is a measure of how steep it is, and it can be calculated using the formula: m = (y2 - y1) / (x2 - x1). The slope of a line is related to its equation, graph, and perpendicular line. We hope that this article has helped to clarify the concept of slope and parallel lines.
Key Takeaways
- The slope of a line is a measure of how steep it is.
- The slope of a line can be calculated using the formula: m = (y2 - y1) / (x2 - x1).
- The slope of a line is related to its equation, graph, and perpendicular line.
- A line can have a slope of 0, 1, -1, or infinity.
- A line can have a negative or positive slope.
- A line can have a slope of 1 or -1.
Frequently Asked Questions
- Q: What is the slope of a line? A: The slope of a line is a measure of how steep it is.
- Q: How do you find the slope of a line? A: To find the slope of a line, you can use the formula: m = (y2 - y1) / (x2 - x1).
- Q: What is the difference between a slope and a y-intercept? A: The slope of a line is a measure of how steep it is, while the y-intercept is the point where the line intersects the y-axis.
Additional Resources
For more information on slope and parallel lines, check out the following resources:
- Khan Academy: Slope and Linear Equations
- Mathway: Slope and Parallel Lines
- Wolfram Alpha: Slope and Parallel Lines