Which of the following is an equation of the line through (11, –3) and (7, 9)? O A y=-x- 20 O . y= x- 0 ос. уз-3х + 30 O D. y = 3x – 12

Algebra and Trigonometry (6th Edition)
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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

Which of the following is an equation of the line through (11, -3) and (7, 9)?

1. A. \( y = -\frac{1}{3}x - \frac{20}{3} \)
2. B. \( y = \frac{1}{3}x - \frac{20}{3} \)
3. C. \( y = -3x + 30 \)
4. D. \( y = 3x - 12 \)

---

The question presents multiple-choice options, asking which equation represents a line passing through the points (11, -3) and (7, 9). To answer this, you would typically calculate the slope of the line using the two points and then use the point-slope form or slope-intercept form to derive the equation of the line.

**Explanation:**

1. **Calculate the Slope:**
   The formula for the slope (\(m\)) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting \((x_1, y_1) = (11, -3)\) and \((x_2, y_2) = (7, 9)\) gives:
   \[
   m = \frac{9 - (-3)}{7 - 11} = \frac{12}{-4} = -3
   \]

2. **Determine the Equation:**
   The general form of the equation of a line is \( y = mx + b \). Using the slope \( m = -3 \) and the point-slope form \( y - y_1 = m(x - x_1) \):
   \[
   y - (-3) = -3(x - 11) \quad \Rightarrow \quad y + 3 = -3(x - 11)
   \]
   Distribute \(-3\):
   \[
   y + 3 = -3x + 33  \quad \Rightarrow \quad y = -3x + 30
   \]

The correct answer is C. \( y =
Transcribed Image Text:Here is a transcription of the provided image for an educational website: --- ### Question Which of the following is an equation of the line through (11, -3) and (7, 9)? 1. A. \( y = -\frac{1}{3}x - \frac{20}{3} \) 2. B. \( y = \frac{1}{3}x - \frac{20}{3} \) 3. C. \( y = -3x + 30 \) 4. D. \( y = 3x - 12 \) --- The question presents multiple-choice options, asking which equation represents a line passing through the points (11, -3) and (7, 9). To answer this, you would typically calculate the slope of the line using the two points and then use the point-slope form or slope-intercept form to derive the equation of the line. **Explanation:** 1. **Calculate the Slope:** The formula for the slope (\(m\)) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting \((x_1, y_1) = (11, -3)\) and \((x_2, y_2) = (7, 9)\) gives: \[ m = \frac{9 - (-3)}{7 - 11} = \frac{12}{-4} = -3 \] 2. **Determine the Equation:** The general form of the equation of a line is \( y = mx + b \). Using the slope \( m = -3 \) and the point-slope form \( y - y_1 = m(x - x_1) \): \[ y - (-3) = -3(x - 11) \quad \Rightarrow \quad y + 3 = -3(x - 11) \] Distribute \(-3\): \[ y + 3 = -3x + 33 \quad \Rightarrow \quad y = -3x + 30 \] The correct answer is C. \( y =
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