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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![**Equation of a Line in Slope-Intercept Form**
**Objective:**
Write the equation of the given line in fully simplified slope-intercept form.
**Graph Details:**
The graph is a coordinate plane with the x-axis ranging from -12 to 12 and the y-axis ranging from -12 to 12. The line is plotted in the blue color, starting from the point (-12, 7) and intersecting the y-axis at approximately (0, 5).
**Steps to Determine the Equation:**
1. **Identify Two Points on the Line:**
- Point A: (-12, 7)
- Point B: (0, 5)
2. **Calculate the Slope (m):**
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 7}{0 - (-12)} = \frac{-2}{12} = -\frac{1}{6}
\]
3. **Use the Slope-Intercept Form (y = mx + b):**
- Substitute the y-intercept (b = 5) and the slope (m = -1/6) into the equation:
\[
y = -\frac{1}{6}x + 5
\]
**Conclusion:**
The equation of the line in fully simplified slope-intercept form is **\( y = -\frac{1}{6}x + 5 \)**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F338f374a-d941-430b-8b7e-f7dd76c88791%2Ff498c997-372e-4af9-a6ee-97ca85458502%2Fyiaa8rh_processed.png&w=3840&q=75)
Transcribed Image Text:**Equation of a Line in Slope-Intercept Form**
**Objective:**
Write the equation of the given line in fully simplified slope-intercept form.
**Graph Details:**
The graph is a coordinate plane with the x-axis ranging from -12 to 12 and the y-axis ranging from -12 to 12. The line is plotted in the blue color, starting from the point (-12, 7) and intersecting the y-axis at approximately (0, 5).
**Steps to Determine the Equation:**
1. **Identify Two Points on the Line:**
- Point A: (-12, 7)
- Point B: (0, 5)
2. **Calculate the Slope (m):**
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 7}{0 - (-12)} = \frac{-2}{12} = -\frac{1}{6}
\]
3. **Use the Slope-Intercept Form (y = mx + b):**
- Substitute the y-intercept (b = 5) and the slope (m = -1/6) into the equation:
\[
y = -\frac{1}{6}x + 5
\]
**Conclusion:**
The equation of the line in fully simplified slope-intercept form is **\( y = -\frac{1}{6}x + 5 \)**.
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