Write the equation of the line that contains the points (0, 3) and (4, 0) in slope-intercept form. Select one: O a. y = 4x +3 O b. y =(-3/4)x+4 O c. y =(-4/3)x+3 O d. y = (-3/4)x+3
Write the equation of the line that contains the points (0, 3) and (4, 0) in slope-intercept form. Select one: O a. y = 4x +3 O b. y =(-3/4)x+4 O c. y =(-4/3)x+3 O d. y = (-3/4)x+3
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,...
Related questions
Question
![### Writing the Equation of a Line
Given Problem:
Write the equation of the line that contains the points (0, 3) and (4, 0) in slope-intercept form.
Choices:
Select one:
- a. \( y = 4x + 3 \)
- b. \( y = \left( -\frac{3}{4} \right) x + 4 \)
- c. \( y = \left( -\frac{4}{3} \right) x + 3 \)
- d. \( y = \left( -\frac{3}{4} \right) x + 3 \)
#### Explanation:
To determine which equation represents the line passing through the points (0, 3) and (4, 0), we can follow these steps:
1. **Calculate the Slope (m):**
The slope of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points (0, 3) and (4, 0):
\[
m = \frac{0 - 3}{4 - 0} = \frac{-3}{4}
\]
2. **Determine the Y-intercept (b):**
Since one of the given points is the y-intercept (0, 3), we can directly use this to find \(b\):
\[
b = 3
\]
3. **Form the Equation in Slope-Intercept Form:**
The equation of the line in slope-intercept form \(y = mx + b\) using the values from above is:
\[
y = \left( -\frac{3}{4} \right) x + 3
\]
Hence, the correct equation is:
- \( \boxed{d. \, y = \left( -\frac{3}{4} \right) x + 3} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bbc26c4-f789-4881-a3b2-dd815a2e0938%2F22c1e82b-8751-49cb-9ae4-9c37b7b4ec22%2Fu5swmdp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Writing the Equation of a Line
Given Problem:
Write the equation of the line that contains the points (0, 3) and (4, 0) in slope-intercept form.
Choices:
Select one:
- a. \( y = 4x + 3 \)
- b. \( y = \left( -\frac{3}{4} \right) x + 4 \)
- c. \( y = \left( -\frac{4}{3} \right) x + 3 \)
- d. \( y = \left( -\frac{3}{4} \right) x + 3 \)
#### Explanation:
To determine which equation represents the line passing through the points (0, 3) and (4, 0), we can follow these steps:
1. **Calculate the Slope (m):**
The slope of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points (0, 3) and (4, 0):
\[
m = \frac{0 - 3}{4 - 0} = \frac{-3}{4}
\]
2. **Determine the Y-intercept (b):**
Since one of the given points is the y-intercept (0, 3), we can directly use this to find \(b\):
\[
b = 3
\]
3. **Form the Equation in Slope-Intercept Form:**
The equation of the line in slope-intercept form \(y = mx + b\) using the values from above is:
\[
y = \left( -\frac{3}{4} \right) x + 3
\]
Hence, the correct equation is:
- \( \boxed{d. \, y = \left( -\frac{3}{4} \right) x + 3} \)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education