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Q) Find an equation of the line Standard Form with x-Intercept 2 and y-Intercept 4.

Q) Find an equation of the line Standard Form with x-Intercept 2 and y-Intercept 4.

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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**Question:** Find an equation of the line in standard form with an x-intercept of 2 and a y-intercept of 4. **Explanation:** To find the equation of a line in standard form, given the x-intercept and y-intercept: 1. **Identify the intercepts**: - The x-intercept is the point (2, 0). - The y-intercept is the point (0, 4). 2. **Use the intercepts to write the equation**: - A line's equation in standard form is \( Ax + By = C \). - Use the intercepts to derive the equation: - Plug x = 2 into the equation and y = 0, which gives \( 2A = C \). - Plug x = 0 into the equation and y = 4, which gives \( 4B = C \). 3. **Solve for coefficients A, B, and C**: - From these equations, solve for values that will satisfy both equations, typically \( A = -2 \), \( B = -1 \), and \( C = -4 \). The exact form may vary. 4. **Equation**: - Substitute back into the equation to verify: \(-2x - y = -4\). This complex technique of using intercepts and solving equations helps in understanding and formulating the equation of a line in standard form.
Transcribed Image Text:**Question:** Find an equation of the line in standard form with an x-intercept of 2 and a y-intercept of 4. **Explanation:** To find the equation of a line in standard form, given the x-intercept and y-intercept: 1. **Identify the intercepts**: - The x-intercept is the point (2, 0). - The y-intercept is the point (0, 4). 2. **Use the intercepts to write the equation**: - A line's equation in standard form is \( Ax + By = C \). - Use the intercepts to derive the equation: - Plug x = 2 into the equation and y = 0, which gives \( 2A = C \). - Plug x = 0 into the equation and y = 4, which gives \( 4B = C \). 3. **Solve for coefficients A, B, and C**: - From these equations, solve for values that will satisfy both equations, typically \( A = -2 \), \( B = -1 \), and \( C = -4 \). The exact form may vary. 4. **Equation**: - Substitute back into the equation to verify: \(-2x - y = -4\). This complex technique of using intercepts and solving equations helps in understanding and formulating the equation of a line in standard form.
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