Find A Point-slope Form For The Line With Slope 1 5 \frac{1}{5} 5 1 And Passing Through The Point ( − 1 , − 9 (-1, -9 ( − 1 , − 9 ].The Equation Of The Line In Point-slope Form Is Y + 9 = 1 5 ( X + 1 Y + 9 = \frac{1}{5}(x + 1 Y + 9 = 5 1 ( X + 1 ]. (Simplify Your Answer. Use Integers Or
Introduction
In mathematics, the point-slope form of a line is a way to express the equation of a line using the slope of the line and a point that lies on the line. This form is particularly useful when we know the slope of the line and a point that it passes through. In this article, we will explore how to find the point-slope form of a line with a given slope and a point that it passes through.
What is the Point-Slope Form?
The point-slope form of a line is given by the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point that lies on the line, and m is the slope of the line. This form is also known as the slope-intercept form, but it is more general and can be used to find the equation of a line even if the slope is not given.
Finding the Point-Slope Form
To find the point-slope form of a line, we need to know the slope of the line and a point that it passes through. Let's consider an example to illustrate this.
Example
Suppose we want to find the point-slope form of a line with a slope of 1/5 and passing through the point (-1, -9). We can use the point-slope form equation to find the equation of the line.
Step 1: Write the Point-Slope Form Equation
The point-slope form equation is:
y - y1 = m(x - x1)
We know that the slope (m) is 1/5, and the point (x1, y1) is (-1, -9). We can substitute these values into the equation:
y - (-9) = (1/5)(x - (-1))
Step 2: Simplify the Equation
We can simplify the equation by combining like terms:
y + 9 = (1/5)(x + 1)
This is the point-slope form of the line.
Conclusion
In this article, we have explored how to find the point-slope form of a line with a given slope and a point that it passes through. We have used the point-slope form equation to find the equation of a line with a slope of 1/5 and passing through the point (-1, -9). The point-slope form is a useful tool for finding the equation of a line, and it can be used in a variety of mathematical applications.
Key Takeaways
- The point-slope form of a line is given by the equation y - y1 = m(x - x1).
- To find the point-slope form of a line, we need to know the slope of the line and a point that it passes through.
- We can use the point-slope form equation to find the equation of a line with a given slope and a point that it passes through.
Further Reading
If you want to learn more about the point-slope form of a line, you can check out the following resources:
- Khan Academy: Point-Slope Form
- Mathway: Point-Slope Form
- Wolfram Alpha: Point-Slope Form
References
- [1] Larson, R. (2014). Algebra and Trigonometry. Cengage Learning.
- [2] Sullivan, M. (2013). Algebra and Trigonometry. Pearson Education.
Glossary
- Point-Slope Form: A way to express the equation of a line using the slope of the line and a point that lies on the line.
- Slope: A measure of how steep a line is.
- Point: A location on a line or a coordinate plane.
FAQs
- Q: What is the point-slope form of a line? A: The point-slope form of a line is given by the equation y - y1 = m(x - x1).
- Q: How do I find the point-slope form of a line? A: To find the point-slope form of a line, you need to know the slope of the line and a point that it passes through.
- Q: Can I use the point-slope form to find the equation of a line with a given slope and a point that it passes through?
A: Yes, you can use the point-slope form equation to find the equation of a line with a given slope and a point that it passes through.
Frequently Asked Questions (FAQs) about Point-Slope Form ===========================================================
Q: What is the point-slope form of a line?
A: The point-slope form of a line is a way to express the equation of a line using the slope of the line and a point that lies on the line. It is given by the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point that lies on the line, and m is the slope of the line.
Q: How do I find the point-slope form of a line?
A: To find the point-slope form of a line, you need to know the slope of the line and a point that it passes through. You can use the point-slope form equation:
y - y1 = m(x - x1)
to find the equation of the line.
Q: Can I use the point-slope form to find the equation of a line with a given slope and a point that it passes through?
A: Yes, you can use the point-slope form equation to find the equation of a line with a given slope and a point that it passes through. For example, if the slope is 1/5 and the point is (-1, -9), you can use the point-slope form equation to find the equation of the line.
Q: How do I simplify the point-slope form equation?
A: To simplify the point-slope form equation, you can combine like terms and rearrange the equation to get it in a more familiar form. For example, if the point-slope form equation is:
y - (-9) = (1/5)(x - (-1))
you can simplify it to:
y + 9 = (1/5)(x + 1)
Q: Can I use the point-slope form to find the equation of a line with a given slope and two points that it passes through?
A: No, the point-slope form is only used to find the equation of a line with a given slope and a single point that it passes through. If you have two points that the line passes through, you can use the two-point form of a line to find the equation of the line.
Q: What is the difference between the point-slope form and the slope-intercept form?
A: The point-slope form and the slope-intercept form are two different ways to express the equation of a line. The point-slope form uses the slope and a point that lies on the line, while the slope-intercept form uses the slope and the y-intercept of the line.
Q: Can I use the point-slope form to find the equation of a line with a given slope and a vertical line?
A: No, the point-slope form is only used to find the equation of a line with a given slope and a non-vertical line. If you have a vertical line, you can use the equation x = a to find the equation of the line.
Q: How do I graph a line using the point-slope form?
A: To graph a line using the point-slope form, you can use the following steps:
- Find the slope of the line.
- Find a point that lies on the line.
- Use the point-slope form equation to find the equation of the line.
- Graph the line using the equation.
Q: Can I use the point-slope form to find the equation of a line with a given slope and a horizontal line?
A: No, the point-slope form is only used to find the equation of a line with a given slope and a non-horizontal line. If you have a horizontal line, you can use the equation y = b to find the equation of the line.
Q: What are some common mistakes to avoid when using the point-slope form?
A: Some common mistakes to avoid when using the point-slope form include:
- Not using the correct slope and point.
- Not simplifying the equation correctly.
- Not using the correct form of the equation (point-slope or slope-intercept).
Q: Can I use the point-slope form to find the equation of a line with a given slope and a line that is not a function?
A: No, the point-slope form is only used to find the equation of a line that is a function. If you have a line that is not a function, you can use the equation of a line that is not a function to find the equation of the line.
Q: How do I check if a line is a function using the point-slope form?
A: To check if a line is a function using the point-slope form, you can use the following steps:
- Find the slope of the line.
- Find a point that lies on the line.
- Use the point-slope form equation to find the equation of the line.
- Check if the equation is in the form y = mx + b, where m is the slope and b is the y-intercept. If it is, then the line is a function. If it is not, then the line is not a function.