Write the equation of the line that contains the points (-2,-3) and (4, 6) in slope-intercept form. Select one: O a. y = (3/2)x O b. y = (3/2)x+6 O c. y =(2/3)x+10/3 O d. y = (3/2)x-3
Write the equation of the line that contains the points (-2,-3) and (4, 6) in slope-intercept form. Select one: O a. y = (3/2)x O b. y = (3/2)x+6 O c. y =(2/3)x+10/3 O d. y = (3/2)x-3
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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![### Equation of a Line: Slope-Intercept Form
**Problem Statement:**
Write the equation of the line that contains the points (-2, -3) and (4, 6) in slope-intercept form.
**Options:**
- a. \( y = \left(\frac{3}{2}\right) x \)
- b. \( y = \left(\frac{3}{2}\right) x + 6 \)
- c. \( y = \left(\frac{2}{3}\right) x + \frac{10}{3} \)
- d. \( y = \left(\frac{3}{2}\right) x - 3 \)
**Explanation:**
To determine which option represents the correct equation of the line in slope-intercept form, we need to find the slope (m) and the y-intercept (b).
1. **Find the slope (m):**
The slope of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the points (-2, -3) and (4, 6):
\[
m = \frac{6 - (-3)}{4 - (-2)} = \frac{6 + 3}{4 + 2} = \frac{9}{6} = \frac{3}{2}
\]
2. **Find the y-intercept (b):**
Use the point-slope form of a line equation \( y = mx + b \) and substitute one of the points along with the slope into the equation to solve for \( b \).
Using the point (4, 6):
\[
6 = \left(\frac{3}{2}\right) \cdot 4 + b
\]
\[
6 = 6 + b
\]
\[
b = 0
\]
Thus, the equation of the line is:
\[
y = \left(\frac{3}{2}\right) x
\]
Therefore, the correct answer is:
- a. \( y = \left(\frac{3}{2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bbc26c4-f789-4881-a3b2-dd815a2e0938%2Fae1ef5c4-02e0-4ca5-8d6f-6bf3ef854369%2Fvju12e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Equation of a Line: Slope-Intercept Form
**Problem Statement:**
Write the equation of the line that contains the points (-2, -3) and (4, 6) in slope-intercept form.
**Options:**
- a. \( y = \left(\frac{3}{2}\right) x \)
- b. \( y = \left(\frac{3}{2}\right) x + 6 \)
- c. \( y = \left(\frac{2}{3}\right) x + \frac{10}{3} \)
- d. \( y = \left(\frac{3}{2}\right) x - 3 \)
**Explanation:**
To determine which option represents the correct equation of the line in slope-intercept form, we need to find the slope (m) and the y-intercept (b).
1. **Find the slope (m):**
The slope of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the points (-2, -3) and (4, 6):
\[
m = \frac{6 - (-3)}{4 - (-2)} = \frac{6 + 3}{4 + 2} = \frac{9}{6} = \frac{3}{2}
\]
2. **Find the y-intercept (b):**
Use the point-slope form of a line equation \( y = mx + b \) and substitute one of the points along with the slope into the equation to solve for \( b \).
Using the point (4, 6):
\[
6 = \left(\frac{3}{2}\right) \cdot 4 + b
\]
\[
6 = 6 + b
\]
\[
b = 0
\]
Thus, the equation of the line is:
\[
y = \left(\frac{3}{2}\right) x
\]
Therefore, the correct answer is:
- a. \( y = \left(\frac{3}{2
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