Write a slope-intercept equation for a line with the given characteristics. m = 2, passes through (1, -8) OA. y=2x-8 B. y = 2x +9 O C. y = 3x +11 D. y=2x-10
Write a slope-intercept equation for a line with the given characteristics. m = 2, passes through (1, -8) OA. y=2x-8 B. y = 2x +9 O C. y = 3x +11 D. y=2x-10
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![## Writing a Slope-Intercept Equation
In this exercise, we are asked to write a slope-intercept equation for a line with the following characteristics:
- **Slope (m):** 2
- **Point the line passes through:** (1, -8)
### Select the Correct Equation
The options provided are:
- **A.** \( y = 2x - 8 \)
- **B.** \( y = 2x + 9 \)
- **C.** \( y = 3x + 11 \)
- **D.** \( y = 2x - 10 \)
To determine which equation is correct, we use the slope-intercept form of a line equation, which is:
\[ y = mx + b \]
Where:
- \( m \) is the slope
- \( b \) is the y-intercept
Using the point (1, -8), substitute x and y into the equation:
\[ -8 = 2(1) + b \]
\[ -8 = 2 + b \]
\[ b = -8 - 2 \]
\[ b = -10 \]
Therefore, the slope-intercept equation for this line is:
\[ y = 2x - 10 \]
### Solution
The correct answer is:
- **D.** \( y = 2x - 10 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e2935af-1329-4dfa-9560-8781a8a0c5be%2Fde5c9733-83aa-4196-aa74-80cc7e6f2559%2Fji1khao_processed.png&w=3840&q=75)
Transcribed Image Text:## Writing a Slope-Intercept Equation
In this exercise, we are asked to write a slope-intercept equation for a line with the following characteristics:
- **Slope (m):** 2
- **Point the line passes through:** (1, -8)
### Select the Correct Equation
The options provided are:
- **A.** \( y = 2x - 8 \)
- **B.** \( y = 2x + 9 \)
- **C.** \( y = 3x + 11 \)
- **D.** \( y = 2x - 10 \)
To determine which equation is correct, we use the slope-intercept form of a line equation, which is:
\[ y = mx + b \]
Where:
- \( m \) is the slope
- \( b \) is the y-intercept
Using the point (1, -8), substitute x and y into the equation:
\[ -8 = 2(1) + b \]
\[ -8 = 2 + b \]
\[ b = -8 - 2 \]
\[ b = -10 \]
Therefore, the slope-intercept equation for this line is:
\[ y = 2x - 10 \]
### Solution
The correct answer is:
- **D.** \( y = 2x - 10 \)
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