**Title: Writing Equations in Point-Slope Form** **Introduction:** In this lesson, we'll explore how to write the equation of a line in point-slope form. This is especially useful when we know the slope of a line and a specific point through which the line passes. **Problem Statement:** A line passes through the point \((8, -5)\) and has a slope of \(-\frac{3}{2}\). Write an equation in point-slope form for this line. **Solution:** To write the equation of a line in point-slope form, we use the formula: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. 1. **Identifying the Given Values:** - Point \((x_1, y_1) = (8, -5)\) - Slope \(m = -\frac{3}{2}\) 2. **Substituting the Values:** We substitute \(x_1\), \(y_1\), and \(m\) into the point-slope form equation: \[ y - (-5) = -\frac{3}{2}(x - 8) \] Simplifying the left side, we get: \[ y + 5 = -\frac{3}{2}(x - 8) \] **Conclusion:** The equation of the line in point-slope form is: \[ y + 5 = -\frac{3}{2}(x - 8) \] This form is very useful for further calculations and graphing. **Exercise:** Try to determine the point-slope form of a line passing through the point \((4, 3)\) with a slope of \(1\). Write down your answer and verify it using the same method shown above. **Graph/Diagram Explanation:** There are three buttons next to the input box. These buttons are used for: 1. Entering an exponent or formatting superscripts. 2. Formatting subscript. 3. Adding fractions. There is also a "Check" button which might be for submitting the answer or verifying the input. Explore these tools to help input your answers correctly!
**Title: Writing Equations in Point-Slope Form** **Introduction:** In this lesson, we'll explore how to write the equation of a line in point-slope form. This is especially useful when we know the slope of a line and a specific point through which the line passes. **Problem Statement:** A line passes through the point \((8, -5)\) and has a slope of \(-\frac{3}{2}\). Write an equation in point-slope form for this line. **Solution:** To write the equation of a line in point-slope form, we use the formula: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. 1. **Identifying the Given Values:** - Point \((x_1, y_1) = (8, -5)\) - Slope \(m = -\frac{3}{2}\) 2. **Substituting the Values:** We substitute \(x_1\), \(y_1\), and \(m\) into the point-slope form equation: \[ y - (-5) = -\frac{3}{2}(x - 8) \] Simplifying the left side, we get: \[ y + 5 = -\frac{3}{2}(x - 8) \] **Conclusion:** The equation of the line in point-slope form is: \[ y + 5 = -\frac{3}{2}(x - 8) \] This form is very useful for further calculations and graphing. **Exercise:** Try to determine the point-slope form of a line passing through the point \((4, 3)\) with a slope of \(1\). Write down your answer and verify it using the same method shown above. **Graph/Diagram Explanation:** There are three buttons next to the input box. These buttons are used for: 1. Entering an exponent or formatting superscripts. 2. Formatting subscript. 3. Adding fractions. There is also a "Check" button which might be for submitting the answer or verifying the input. Explore these tools to help input your answers correctly!
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Title: Writing Equations in Point-Slope Form**
**Introduction:**
In this lesson, we'll explore how to write the equation of a line in point-slope form. This is especially useful when we know the slope of a line and a specific point through which the line passes.
**Problem Statement:**
A line passes through the point \((8, -5)\) and has a slope of \(-\frac{3}{2}\). Write an equation in point-slope form for this line.
**Solution:**
To write the equation of a line in point-slope form, we use the formula:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
1. **Identifying the Given Values:**
- Point \((x_1, y_1) = (8, -5)\)
- Slope \(m = -\frac{3}{2}\)
2. **Substituting the Values:**
We substitute \(x_1\), \(y_1\), and \(m\) into the point-slope form equation:
\[
y - (-5) = -\frac{3}{2}(x - 8)
\]
Simplifying the left side, we get:
\[
y + 5 = -\frac{3}{2}(x - 8)
\]
**Conclusion:**
The equation of the line in point-slope form is:
\[
y + 5 = -\frac{3}{2}(x - 8)
\]
This form is very useful for further calculations and graphing.
**Exercise:**
Try to determine the point-slope form of a line passing through the point \((4, 3)\) with a slope of \(1\). Write down your answer and verify it using the same method shown above.
**Graph/Diagram Explanation:**
There are three buttons next to the input box. These buttons are used for:
1. Entering an exponent or formatting superscripts.
2. Formatting subscript.
3. Adding fractions.
There is also a "Check" button which might be for submitting the answer or verifying the input.
Explore these tools to help input your answers correctly!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2a0c424-9580-4921-9cbc-e3b4792ff10b%2F0fc9bc1e-6801-4958-a86d-2407c1870112%2Fevsa7vc.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Writing Equations in Point-Slope Form**
**Introduction:**
In this lesson, we'll explore how to write the equation of a line in point-slope form. This is especially useful when we know the slope of a line and a specific point through which the line passes.
**Problem Statement:**
A line passes through the point \((8, -5)\) and has a slope of \(-\frac{3}{2}\). Write an equation in point-slope form for this line.
**Solution:**
To write the equation of a line in point-slope form, we use the formula:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
1. **Identifying the Given Values:**
- Point \((x_1, y_1) = (8, -5)\)
- Slope \(m = -\frac{3}{2}\)
2. **Substituting the Values:**
We substitute \(x_1\), \(y_1\), and \(m\) into the point-slope form equation:
\[
y - (-5) = -\frac{3}{2}(x - 8)
\]
Simplifying the left side, we get:
\[
y + 5 = -\frac{3}{2}(x - 8)
\]
**Conclusion:**
The equation of the line in point-slope form is:
\[
y + 5 = -\frac{3}{2}(x - 8)
\]
This form is very useful for further calculations and graphing.
**Exercise:**
Try to determine the point-slope form of a line passing through the point \((4, 3)\) with a slope of \(1\). Write down your answer and verify it using the same method shown above.
**Graph/Diagram Explanation:**
There are three buttons next to the input box. These buttons are used for:
1. Entering an exponent or formatting superscripts.
2. Formatting subscript.
3. Adding fractions.
There is also a "Check" button which might be for submitting the answer or verifying the input.
Explore these tools to help input your answers correctly!
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