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Line I is shown below. Right triangles ABC and DEF are drawn to measure the slope of the line. D F .4..6..8..10..12. 14. 15 18. 20...22.

Line I is shown below. Right triangles ABC and DEF are drawn to measure the slope of the line. D F .4..6..8..10..12. 14. 15 18. 20...22.

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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Line \( l \) is shown below. Right triangles \( ABC \) and \( DEF \) are drawn to measure the slope of the line. **Graph Description:** The graph is a coordinate plane with a line \( l \) passing through it. The line is inclined upwards from left to right. Two right triangles, \( ABC \) and \( DEF \), are drawn along the line to measure its slope. 1. **Triangle \( ABC \):** - Point \( A \) is on the line. - Point \( B \) is directly below \( A \) on the x-axis. - Point \( C \) is directly to the left of \( B \) on the y-axis. - The triangle's right angle is at point \( B \). 2. **Triangle \( DEF \):** - Point \( D \) is on the line. - Point \( E \) is directly below \( D \) on the x-axis. - Point \( F \) is directly to the left of \( E \) on the y-axis. - The triangle's right angle is at point \( E \). Both right triangles share the same hypotenuse as part of line \( l \), and they demonstrate how the rise over run ratio is constant, representing the slope of the line.
Transcribed Image Text:Line \( l \) is shown below. Right triangles \( ABC \) and \( DEF \) are drawn to measure the slope of the line. **Graph Description:** The graph is a coordinate plane with a line \( l \) passing through it. The line is inclined upwards from left to right. Two right triangles, \( ABC \) and \( DEF \), are drawn along the line to measure its slope. 1. **Triangle \( ABC \):** - Point \( A \) is on the line. - Point \( B \) is directly below \( A \) on the x-axis. - Point \( C \) is directly to the left of \( B \) on the y-axis. - The triangle's right angle is at point \( B \). 2. **Triangle \( DEF \):** - Point \( D \) is on the line. - Point \( E \) is directly below \( D \) on the x-axis. - Point \( F \) is directly to the left of \( E \) on the y-axis. - The triangle's right angle is at point \( E \). Both right triangles share the same hypotenuse as part of line \( l \), and they demonstrate how the rise over run ratio is constant, representing the slope of the line.
**Complete the parts below.** (a) Find the run, rise, and slope given by triangle \( ABC \). - **run:** [ ] - **rise:** [ ] - **slope:** [ ] (b) Find the run, rise, and slope given by triangle \( DEF \). - **run:** [ ] - **rise:** [ ] - **slope:** [ ] (c) Are the two slopes computed above equal? Why or why not? - ( ) Yes. They are equal because the two triangles are similar. - ( ) Yes. They are equal because the two triangles are congruent. - ( ) No. They are not equal because the larger the triangle, the larger the slope. - ( ) No. They are not equal because the smaller the triangle, the smaller the slope.
Transcribed Image Text:**Complete the parts below.** (a) Find the run, rise, and slope given by triangle \( ABC \). - **run:** [ ] - **rise:** [ ] - **slope:** [ ] (b) Find the run, rise, and slope given by triangle \( DEF \). - **run:** [ ] - **rise:** [ ] - **slope:** [ ] (c) Are the two slopes computed above equal? Why or why not? - ( ) Yes. They are equal because the two triangles are similar. - ( ) Yes. They are equal because the two triangles are congruent. - ( ) No. They are not equal because the larger the triangle, the larger the slope. - ( ) No. They are not equal because the smaller the triangle, the smaller the slope.
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