L-L-2) Example 15 Plug (-2,- Find the equation of the line: awith gradient-2 and passing through (-4, 3) b passing through (-2,-1) and (6,-5). Write down the equations in the gradient-intercept form y mx + k. where m is the gradient and k is the y-coordinate of the y-intercept. Finad K
L-L-2) Example 15 Plug (-2,- Find the equation of the line: awith gradient-2 and passing through (-4, 3) b passing through (-2,-1) and (6,-5). Write down the equations in the gradient-intercept form y mx + k. where m is the gradient and k is the y-coordinate of the y-intercept. Finad K
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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![**Example 15**
**Find the equation of the line:**
**a.** with gradient -2 and passing through (-4, 3)
**b.** passing through (-2, -1) and (6, -5).
Write down the equations in the gradient-intercept form \( y = mx + k \), where \( m \) is the gradient and \( k \) is the y-coordinate of the y-intercept.
### Solution:
1. **Gradient Calculation for Part (b):**
\[
m = \frac{\text{rise}}{\text{run}} = \frac{-5 - (-1)}{6 - (-2)} = \frac{-4}{8} = -\frac{1}{2}
\]
2. **Equation Formulation:**
\[
y = -\frac{1}{2}x + k
\]
Use point (-2, -1) to find \( k \).
### Graphs:
There are two empty graph grids provided for plotting the equations visually. Each graph has labeled axes ready for inserting lines.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb4562d2-ab10-49bf-b0aa-7e3eca82fcb1%2F7c274e8c-d5e6-4748-bc0e-2c2f21176b86%2Fc2m9fib_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example 15**
**Find the equation of the line:**
**a.** with gradient -2 and passing through (-4, 3)
**b.** passing through (-2, -1) and (6, -5).
Write down the equations in the gradient-intercept form \( y = mx + k \), where \( m \) is the gradient and \( k \) is the y-coordinate of the y-intercept.
### Solution:
1. **Gradient Calculation for Part (b):**
\[
m = \frac{\text{rise}}{\text{run}} = \frac{-5 - (-1)}{6 - (-2)} = \frac{-4}{8} = -\frac{1}{2}
\]
2. **Equation Formulation:**
\[
y = -\frac{1}{2}x + k
\]
Use point (-2, -1) to find \( k \).
### Graphs:
There are two empty graph grids provided for plotting the equations visually. Each graph has labeled axes ready for inserting lines.
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