Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is +=1, a +0, b #0. a x-intercept: (, 0) y-intercept: (0, –6)
Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is +=1, a +0, b #0. a x-intercept: (, 0) y-intercept: (0, –6)
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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![**Finding the Equation of a Line Using the Intercept Form**
**Overview:**
Learn how to find the equation of a line using the intercept form, given its intercepts with the x-axis and y-axis.
**Intercept Form of a Line:**
The intercept form of a line with x-intercept \((a, 0)\) and y-intercept \((0, b)\) is given by the equation:
\[
\frac{x}{a} + \frac{y}{b} = 1, \quad a \neq 0, \, b \neq 0.
\]
**Given Intercepts:**
- x-intercept: \(\left(-\frac{2}{3}, 0\right)\)
- y-intercept: \((0, -6)\)
**Question:**
Using the given intercepts, identify the correct equation of the line from the options below:
- \((-18x - 3y - 2 = 0\))
- \(18x + 3y - 2 = 0\)
- \(-18x + 3y + 2 = 0\)
- \(18x + 2y + 12 = 0\)
- \(18x - 3y + 2 = 0\)
Select the correct equation by substituting the intercepts into the intercept form equation and simplifying.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c568328-9c88-4125-9322-2592809e36a0%2F6496729e-d016-48b4-bb0c-7396bf2596c6%2F9i7ix6_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Equation of a Line Using the Intercept Form**
**Overview:**
Learn how to find the equation of a line using the intercept form, given its intercepts with the x-axis and y-axis.
**Intercept Form of a Line:**
The intercept form of a line with x-intercept \((a, 0)\) and y-intercept \((0, b)\) is given by the equation:
\[
\frac{x}{a} + \frac{y}{b} = 1, \quad a \neq 0, \, b \neq 0.
\]
**Given Intercepts:**
- x-intercept: \(\left(-\frac{2}{3}, 0\right)\)
- y-intercept: \((0, -6)\)
**Question:**
Using the given intercepts, identify the correct equation of the line from the options below:
- \((-18x - 3y - 2 = 0\))
- \(18x + 3y - 2 = 0\)
- \(-18x + 3y + 2 = 0\)
- \(18x + 2y + 12 = 0\)
- \(18x - 3y + 2 = 0\)
Select the correct equation by substituting the intercepts into the intercept form equation and simplifying.
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