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Graph x + y = 4 on the coordinate system below showing the graph of y = 3 At what points do the graphs intersect? 6+ 5+ 4- 3+ 2- 5 4 -3 -2 -1 2 4 5 -2+ -3+ -4 45- Clear All Draw: Points of intersection: 3.

Graph x + y = 4 on the coordinate system below showing the graph of y = 3 At what points do the graphs intersect? 6+ 5+ 4- 3+ 2- 5 4 -3 -2 -1 2 4 5 -2+ -3+ -4 45- Clear All Draw: Points of intersection: 3.

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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**Problem Statement:** Graph \( x + y = 4 \) on the coordinate system below showing the graph of \( y = \frac{3}{x} \). At what points do the graphs intersect? **Graph Description:** The graph consists of two functions: 1. **Linear Function**: The equation \( x + y = 4 \) is a straight line with a negative slope. To graph this, you can rearrange the equation as \( y = -x + 4 \). 2. **Hyperbolic Function**: The equation \( y = \frac{3}{x} \) is a hyperbola that approaches the axes but never touches them. The hyperbola has two branches separated by the y-axis. **Coordinate Grid:** - The graph is plotted on a standard Cartesian coordinate system with both x and y axes ranging from approximately -8 to 8. - The grid lines are evenly spaced, indicating increments of 1 unit. **Graph Interaction:** There is a section titled "Draw" with buttons for adding lines, curves, and shapes, along with a "Clear All" button. **Points of Intersection Section:** - There is a text box labeled "Points of intersection:" where you can list the coordinates of the intersection points of the given graphs. **Task:** Find the intersection points of the graphs of the linear equation \( x + y = 4 \) and the hyperbolic equation \( y = \frac{3}{x} \).
Transcribed Image Text:**Problem Statement:** Graph \( x + y = 4 \) on the coordinate system below showing the graph of \( y = \frac{3}{x} \). At what points do the graphs intersect? **Graph Description:** The graph consists of two functions: 1. **Linear Function**: The equation \( x + y = 4 \) is a straight line with a negative slope. To graph this, you can rearrange the equation as \( y = -x + 4 \). 2. **Hyperbolic Function**: The equation \( y = \frac{3}{x} \) is a hyperbola that approaches the axes but never touches them. The hyperbola has two branches separated by the y-axis. **Coordinate Grid:** - The graph is plotted on a standard Cartesian coordinate system with both x and y axes ranging from approximately -8 to 8. - The grid lines are evenly spaced, indicating increments of 1 unit. **Graph Interaction:** There is a section titled "Draw" with buttons for adding lines, curves, and shapes, along with a "Clear All" button. **Points of Intersection Section:** - There is a text box labeled "Points of intersection:" where you can list the coordinates of the intersection points of the given graphs. **Task:** Find the intersection points of the graphs of the linear equation \( x + y = 4 \) and the hyperbolic equation \( y = \frac{3}{x} \).
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