What is the slope-intercept equation for the linear function represented by the table? X 03 6 9 12 y 3 1 -1 -3 -5 A. y = -x - 3 B. y = x - 3 c. y = OD. y = x +3 x +3
What is the slope-intercept equation for the linear function represented by the table? X 03 6 9 12 y 3 1 -1 -3 -5 A. y = -x - 3 B. y = x - 3 c. y = OD. y = x +3 x +3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![---
### Slope-Intercept Equation of a Linear Function
**Question:**
What is the slope-intercept equation for the linear function represented by the table?
**Table:**
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 0 & 3 & 6 & 9 & 12 \\
\hline
y & 3 & 1 & -1 & -3 & -5 \\
\hline
\end{array}
\]
**Options:**
A. \( y = -\frac{2}{3}x - 3 \)
B. \( y = \frac{2}{3}x - 3 \)
C. \( y = -\frac{2}{3}x + 3 \)
D. \( y = \frac{2}{3}x + 3 \)
---
To determine the slope-intercept equation of a linear function, we need to find the slope (\(m\)) and the y-intercept (\(b\)) of the line. The general form of the slope-intercept equation is:
\[
y = mx + b
\]
Let's calculate the slope (\(m\)):
The slope of the line is given by the formula:
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 3) and (3, 1):
\[
m = \frac{1 - 3}{3 - 0} = \frac{-2}{3}
\]
So, the slope (\(m\)) is \(-\frac{2}{3}\).
Next, let's find the y-intercept (\(b\)). The y-intercept is the value of \(y\) when \(x = 0\), which is given directly in the table as \(3\).
Substituting these values into the slope-intercept form equation:
\[
y = -\frac{2}{3}x + 3
\]
Therefore, the correct equation is:
C. \( y = -\frac{2}{3}x + 3 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02754e96-2623-4a34-8cc6-772025d5d216%2Fb5009ba7-65cb-44ff-a64d-6eab18ab631f%2Fx2kzk6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Slope-Intercept Equation of a Linear Function
**Question:**
What is the slope-intercept equation for the linear function represented by the table?
**Table:**
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 0 & 3 & 6 & 9 & 12 \\
\hline
y & 3 & 1 & -1 & -3 & -5 \\
\hline
\end{array}
\]
**Options:**
A. \( y = -\frac{2}{3}x - 3 \)
B. \( y = \frac{2}{3}x - 3 \)
C. \( y = -\frac{2}{3}x + 3 \)
D. \( y = \frac{2}{3}x + 3 \)
---
To determine the slope-intercept equation of a linear function, we need to find the slope (\(m\)) and the y-intercept (\(b\)) of the line. The general form of the slope-intercept equation is:
\[
y = mx + b
\]
Let's calculate the slope (\(m\)):
The slope of the line is given by the formula:
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 3) and (3, 1):
\[
m = \frac{1 - 3}{3 - 0} = \frac{-2}{3}
\]
So, the slope (\(m\)) is \(-\frac{2}{3}\).
Next, let's find the y-intercept (\(b\)). The y-intercept is the value of \(y\) when \(x = 0\), which is given directly in the table as \(3\).
Substituting these values into the slope-intercept form equation:
\[
y = -\frac{2}{3}x + 3
\]
Therefore, the correct equation is:
C. \( y = -\frac{2}{3}x + 3 \)
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 with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
