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### Educational Content on Slopes and Perpendicular Lines #### Question 2 **Problem:** The slope of a line is \( \frac{4}{5} \). What is the slope of a line that is perpendicular to it? **Options:** - A. \( \frac{-4}{5} \) - B. \( \frac{4}{5} \) - C. \( \frac{5}{4} \) - D. \( \frac{-5}{4} \) **Explanation:** To find the slope of a line that is perpendicular to a given line, take the negative reciprocal of the original slope. Thus, the answer is: - **D. \( \frac{-5}{4} \)** #### Question 3 **Task:** Write an equation in slope-intercept form for the line that passes through the point \( (5, -4) \). **Instructions:** For credit, make sure to show all of your steps to arrive at your final equation. Explain what you did in each step to ensure clarity and understanding. **General Steps:** 1. Use the point-slope form of a line equation: \( y - y_1 = m(x - x_1) \). 2. Substitute the given point into the equation. 3. Rearrange to find the slope-intercept form: \( y = mx + b \). **Note:** The specific steps to solve this problem were not provided in the image, so these are general guidelines based on the task given. **Question 1** Which of the following equations describes a line parallel to the line graphed below? (Graph Description: The graph shows a line with a negative slope passing through the y-axis at approximately y = 3 and x-axis at approximately x = 4. The graph is on a coordinate plane with grid lines.) - A. \( -4x + y = -7 \) - B. \( y = -3x + 2 \) - C. \( y = -4x - 3 \) - D. \( 4x + 3y = -6 \) **Question 2** The slope of a line is \( \frac{4}{5} \). What is the slope of a line that is perpendicular to it? - A. \( -\frac{4}{5} \) - B. \( -\frac{5}{4} \) - C. \( \frac{5}{4} \) - D. \( \frac{4}{5} \) *Instructions: Click Save and Submit to save and submit. Click Save All Answers to save all answers.*

### Educational Content on Slopes and Perpendicular Lines #### Question 2 **Problem:** The slope of a line is \( \frac{4}{5} \). What is the slope of a line that is perpendicular to it? **Options:** - A. \( \frac{-4}{5} \) - B. \( \frac{4}{5} \) - C. \( \frac{5}{4} \) - D. \( \frac{-5}{4} \) **Explanation:** To find the slope of a line that is perpendicular to a given line, take the negative reciprocal of the original slope. Thus, the answer is: - **D. \( \frac{-5}{4} \)** #### Question 3 **Task:** Write an equation in slope-intercept form for the line that passes through the point \( (5, -4) \). **Instructions:** For credit, make sure to show all of your steps to arrive at your final equation. Explain what you did in each step to ensure clarity and understanding. **General Steps:** 1. Use the point-slope form of a line equation: \( y - y_1 = m(x - x_1) \). 2. Substitute the given point into the equation. 3. Rearrange to find the slope-intercept form: \( y = mx + b \). **Note:** The specific steps to solve this problem were not provided in the image, so these are general guidelines based on the task given. **Question 1** Which of the following equations describes a line parallel to the line graphed below? (Graph Description: The graph shows a line with a negative slope passing through the y-axis at approximately y = 3 and x-axis at approximately x = 4. The graph is on a coordinate plane with grid lines.) - A. \( -4x + y = -7 \) - B. \( y = -3x + 2 \) - C. \( y = -4x - 3 \) - D. \( 4x + 3y = -6 \) **Question 2** The slope of a line is \( \frac{4}{5} \). What is the slope of a line that is perpendicular to it? - A. \( -\frac{4}{5} \) - B. \( -\frac{5}{4} \) - C. \( \frac{5}{4} \) - D. \( \frac{4}{5} \) *Instructions: Click Save and Submit to save and submit. Click Save All Answers to save all answers.*

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Educational Content on Slopes and Perpendicular Lines #### Question 2 **Problem:** The slope of a line is \( \frac{4}{5} \). What is the slope of a line that is perpendicular to it? **Options:** - A. \( \frac{-4}{5} \) - B. \( \frac{4}{5} \) - C. \( \frac{5}{4} \) - D. \( \frac{-5}{4} \) **Explanation:** To find the slope of a line that is perpendicular to a given line, take the negative reciprocal of the original slope. Thus, the answer is: - **D. \( \frac{-5}{4} \)** #### Question 3 **Task:** Write an equation in slope-intercept form for the line that passes through the point \( (5, -4) \). **Instructions:** For credit, make sure to show all of your steps to arrive at your final equation. Explain what you did in each step to ensure clarity and understanding. **General Steps:** 1. Use the point-slope form of a line equation: \( y - y_1 = m(x - x_1) \). 2. Substitute the given point into the equation. 3. Rearrange to find the slope-intercept form: \( y = mx + b \). **Note:** The specific steps to solve this problem were not provided in the image, so these are general guidelines based on the task given.
Transcribed Image Text:### Educational Content on Slopes and Perpendicular Lines #### Question 2 **Problem:** The slope of a line is \( \frac{4}{5} \). What is the slope of a line that is perpendicular to it? **Options:** - A. \( \frac{-4}{5} \) - B. \( \frac{4}{5} \) - C. \( \frac{5}{4} \) - D. \( \frac{-5}{4} \) **Explanation:** To find the slope of a line that is perpendicular to a given line, take the negative reciprocal of the original slope. Thus, the answer is: - **D. \( \frac{-5}{4} \)** #### Question 3 **Task:** Write an equation in slope-intercept form for the line that passes through the point \( (5, -4) \). **Instructions:** For credit, make sure to show all of your steps to arrive at your final equation. Explain what you did in each step to ensure clarity and understanding. **General Steps:** 1. Use the point-slope form of a line equation: \( y - y_1 = m(x - x_1) \). 2. Substitute the given point into the equation. 3. Rearrange to find the slope-intercept form: \( y = mx + b \). **Note:** The specific steps to solve this problem were not provided in the image, so these are general guidelines based on the task given.
**Question 1** Which of the following equations describes a line parallel to the line graphed below? (Graph Description: The graph shows a line with a negative slope passing through the y-axis at approximately y = 3 and x-axis at approximately x = 4. The graph is on a coordinate plane with grid lines.) - A. \( -4x + y = -7 \) - B. \( y = -3x + 2 \) - C. \( y = -4x - 3 \) - D. \( 4x + 3y = -6 \) **Question 2** The slope of a line is \( \frac{4}{5} \). What is the slope of a line that is perpendicular to it? - A. \( -\frac{4}{5} \) - B. \( -\frac{5}{4} \) - C. \( \frac{5}{4} \) - D. \( \frac{4}{5} \) *Instructions: Click Save and Submit to save and submit. Click Save All Answers to save all answers.*
Transcribed Image Text:**Question 1** Which of the following equations describes a line parallel to the line graphed below? (Graph Description: The graph shows a line with a negative slope passing through the y-axis at approximately y = 3 and x-axis at approximately x = 4. The graph is on a coordinate plane with grid lines.) - A. \( -4x + y = -7 \) - B. \( y = -3x + 2 \) - C. \( y = -4x - 3 \) - D. \( 4x + 3y = -6 \) **Question 2** The slope of a line is \( \frac{4}{5} \). What is the slope of a line that is perpendicular to it? - A. \( -\frac{4}{5} \) - B. \( -\frac{5}{4} \) - C. \( \frac{5}{4} \) - D. \( \frac{4}{5} \) *Instructions: Click Save and Submit to save and submit. Click Save All Answers to save all answers.*
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