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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![### Problem Statement:
**Objective:** Find an equation of the line that goes through the points (10, -21) and (-2, 3). Write your answer in the form \( y = mx + b \).
**Answer box:**
\[ y = \_\_\_\_\_ \]
### Steps to Solve:
1. **Find the slope \( m \):**
Use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
2. **Substitute the points into the slope formula:**
For points (10, -21) and (-2, 3):
\[
m = \frac{3 - (-21)}{-2 - 10} = \frac{3 + 21}{-2 - 10} = \frac{24}{-12} = -2
\]
3. **Use the point-slope form to find the y-intercept \( b \):**
Point-slope form equation:
\[
y - y_1 = m(x - x_1)
\]
Using point (10, -21):
\[
y + 21 = -2(x - 10)
\]
Simplify to form \( y = mx + b \):
\[
y + 21 = -2x + 20
\]
\[
y = -2x + 20 - 21
\]
\[
y = -2x - 1
\]
### Final Answer:
\[ y = -2x - 1 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcebbde0b-56df-456f-b45f-057baf1d3a0f%2F65dceeb2-f4fd-43ff-81bf-0df7280b9c0d%2Ft01gs27_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
**Objective:** Find an equation of the line that goes through the points (10, -21) and (-2, 3). Write your answer in the form \( y = mx + b \).
**Answer box:**
\[ y = \_\_\_\_\_ \]
### Steps to Solve:
1. **Find the slope \( m \):**
Use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
2. **Substitute the points into the slope formula:**
For points (10, -21) and (-2, 3):
\[
m = \frac{3 - (-21)}{-2 - 10} = \frac{3 + 21}{-2 - 10} = \frac{24}{-12} = -2
\]
3. **Use the point-slope form to find the y-intercept \( b \):**
Point-slope form equation:
\[
y - y_1 = m(x - x_1)
\]
Using point (10, -21):
\[
y + 21 = -2(x - 10)
\]
Simplify to form \( y = mx + b \):
\[
y + 21 = -2x + 20
\]
\[
y = -2x + 20 - 21
\]
\[
y = -2x - 1
\]
### Final Answer:
\[ y = -2x - 1 \]
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