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Use the intercept form to find the general form of 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 x + x = 1, a = 0, b = 0. a b 1 Point on line: (8,7) x-intercept: (c, 0), c = 0 y-intercept: (0, c), c = 0 X

Use the intercept form to find the general form of 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 x + x = 1, a = 0, b = 0. a b 1 Point on line: (8,7) x-intercept: (c, 0), c = 0 y-intercept: (0, c), c = 0 X

Algebra and Trigonometry (6th Edition)
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,...
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## Finding the General Form of the Equation of a Line Using Intercepts ### Intercept Form To find the general form of the equation of a line using the intercept form, we begin with understanding the intercept form of the equation of a line. The intercept form for a line with intercepts \( (a, 0) \) and \( (0, b) \) is given by: \[ \frac{X}{a} + \frac{Y}{b} = 1 \] where \( a \neq 0 \) and \( b \neq 0 \). ### Example Consider the following information given for a specific line: - **Point on line**: \( (8, 7) \) - **x-intercept**: \( (c, 0) \), where \( c \ne 0 \) - **y-intercept**: \( (0, c) \), where \( c \ne 0 \) You can use these provided intercepts and the point to determine the intercept form and consequently find the general form of the equation of the line. ### Detailed Explanation 1. **Intercept Form Equation**: Start with the intercept form equation: \[ \frac{X}{a} + \frac{Y}{b} = 1 \] 2. **Substitute Intercepts**: Suppose the equation is given through specific intercepts for x and y a given point. For \( a \) as the x-intercept and \( b \) as the y-intercept, replace these into the equation. 3. **Point Substitution**: Substitute the given point \( (8, 7) \) into the equation and solve for any unknowns if needed. ### Graphical Explanation In the context of a graphical understanding: - The x-intercept \( (c, 0) \): This is the point where the line meets the x-axis. - The y-intercept \( (0, c) \): This is the point where the line meets the y-axis. The intercept form allows straightforward visualization of how a line interacts with the axis based on known intercepts. ### Box and Cross Marks - There's a box which might be meant for inputting a value, indicating a practice problem or quiz. - A red cross mark likely indicates an incorrect answer for the value entered. By understanding and using the intercept form, students can find and derive various forms of line
Transcribed Image Text:## Finding the General Form of the Equation of a Line Using Intercepts ### Intercept Form To find the general form of the equation of a line using the intercept form, we begin with understanding the intercept form of the equation of a line. The intercept form for a line with intercepts \( (a, 0) \) and \( (0, b) \) is given by: \[ \frac{X}{a} + \frac{Y}{b} = 1 \] where \( a \neq 0 \) and \( b \neq 0 \). ### Example Consider the following information given for a specific line: - **Point on line**: \( (8, 7) \) - **x-intercept**: \( (c, 0) \), where \( c \ne 0 \) - **y-intercept**: \( (0, c) \), where \( c \ne 0 \) You can use these provided intercepts and the point to determine the intercept form and consequently find the general form of the equation of the line. ### Detailed Explanation 1. **Intercept Form Equation**: Start with the intercept form equation: \[ \frac{X}{a} + \frac{Y}{b} = 1 \] 2. **Substitute Intercepts**: Suppose the equation is given through specific intercepts for x and y a given point. For \( a \) as the x-intercept and \( b \) as the y-intercept, replace these into the equation. 3. **Point Substitution**: Substitute the given point \( (8, 7) \) into the equation and solve for any unknowns if needed. ### Graphical Explanation In the context of a graphical understanding: - The x-intercept \( (c, 0) \): This is the point where the line meets the x-axis. - The y-intercept \( (0, c) \): This is the point where the line meets the y-axis. The intercept form allows straightforward visualization of how a line interacts with the axis based on known intercepts. ### Box and Cross Marks - There's a box which might be meant for inputting a value, indicating a practice problem or quiz. - A red cross mark likely indicates an incorrect answer for the value entered. By understanding and using the intercept form, students can find and derive various forms of line
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