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7. : Find the point of intersection of the two lines L: 3x - 4y = 2 M: x +2y = 4 Graph the lines.

7. : Find the point of intersection of the two lines L: 3x - 4y = 2 M: x +2y = 4 Graph the lines.

Calculus: Early Transcendentals
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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### Mathematical Problems for Educational Practice #### Problem 6: Dan receives $\(S\) per week for selling new and used cars at a car dealership. In addition to his weekly salary, he receives 5% of the profit on any sales he generates. Write an equation that relates Dan's weekly salary \(S\) when he makes sales that generate a profit of \(x\) dollars. #### Problem 7: Find the point of intersection of the two lines: Line \(L\): \(3x - 4y = 2\) Line \(M\): \(x + 2y = 4\) **Task:** Graph the lines. **Explanation for Graphs and Diagrams:** - Start by rewriting each equation in slope-intercept form (\(y = mx + b\)). - For Line \(L\): - \(3x - 4y = 2\) can be rewritten as \(y = \frac{3}{4}x - \frac{1}{2}\). - For Line \(M\): - \(x + 2y = 4\) can be rewritten as \(y = -\frac{1}{2}x + 2\). - Plot these lines on a coordinate plane. - The point where these two lines intersect each other is the solution to both equations. This point is the solution for the system of linear equations given by the lines \(L\) and \(M\).
Transcribed Image Text:### Mathematical Problems for Educational Practice #### Problem 6: Dan receives $\(S\) per week for selling new and used cars at a car dealership. In addition to his weekly salary, he receives 5% of the profit on any sales he generates. Write an equation that relates Dan's weekly salary \(S\) when he makes sales that generate a profit of \(x\) dollars. #### Problem 7: Find the point of intersection of the two lines: Line \(L\): \(3x - 4y = 2\) Line \(M\): \(x + 2y = 4\) **Task:** Graph the lines. **Explanation for Graphs and Diagrams:** - Start by rewriting each equation in slope-intercept form (\(y = mx + b\)). - For Line \(L\): - \(3x - 4y = 2\) can be rewritten as \(y = \frac{3}{4}x - \frac{1}{2}\). - For Line \(M\): - \(x + 2y = 4\) can be rewritten as \(y = -\frac{1}{2}x + 2\). - Plot these lines on a coordinate plane. - The point where these two lines intersect each other is the solution to both equations. This point is the solution for the system of linear equations given by the lines \(L\) and \(M\).
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