Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To determine the equation of a line given its slope and [tex]\( y \)[/tex]-intercept, we use the slope-intercept form of a linear equation, which is:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope of the line,
- [tex]\( b \)[/tex] is the [tex]\( y \)[/tex]-intercept.
### Step-by-Step Solution:
1. Identify the given values:
- The slope ([tex]\( m \)[/tex]) is [tex]\(\frac{3}{2}\)[/tex].
- The [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is [tex]\(-12\)[/tex].
2. Substitute these values into the slope-intercept form:
- The slope-intercept form equation is [tex]\( y = mx + b \)[/tex].
- Plug in the slope [tex]\( m = \frac{3}{2} \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\( b = -12 \)[/tex].
[tex]\[ y = \left(\frac{3}{2}\right)x + (-12) \][/tex]
[tex]\[ y = \left(\frac{3}{2}\right)x - 12 \][/tex]
3. Match this equation with the provided options:
- A. [tex]\( y = \frac{3}{2} x - 12 \)[/tex]
- B. [tex]\( y = \frac{3}{2} x + 12 \)[/tex]
- C. [tex]\( y = \frac{2}{3} x - 12 \)[/tex]
- D. [tex]\( y = -12 x - \frac{3}{2} \)[/tex]
The correct equation that matches our derived equation is:
[tex]\[ \boxed{y = \frac{3}{2} x - 12} \][/tex]
Thus, the correct answer is A.
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope of the line,
- [tex]\( b \)[/tex] is the [tex]\( y \)[/tex]-intercept.
### Step-by-Step Solution:
1. Identify the given values:
- The slope ([tex]\( m \)[/tex]) is [tex]\(\frac{3}{2}\)[/tex].
- The [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is [tex]\(-12\)[/tex].
2. Substitute these values into the slope-intercept form:
- The slope-intercept form equation is [tex]\( y = mx + b \)[/tex].
- Plug in the slope [tex]\( m = \frac{3}{2} \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\( b = -12 \)[/tex].
[tex]\[ y = \left(\frac{3}{2}\right)x + (-12) \][/tex]
[tex]\[ y = \left(\frac{3}{2}\right)x - 12 \][/tex]
3. Match this equation with the provided options:
- A. [tex]\( y = \frac{3}{2} x - 12 \)[/tex]
- B. [tex]\( y = \frac{3}{2} x + 12 \)[/tex]
- C. [tex]\( y = \frac{2}{3} x - 12 \)[/tex]
- D. [tex]\( y = -12 x - \frac{3}{2} \)[/tex]
The correct equation that matches our derived equation is:
[tex]\[ \boxed{y = \frac{3}{2} x - 12} \][/tex]
Thus, the correct answer is A.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.