Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Certainly! Let's go through the steps to convert the given equation from Standard Form to Slope-Intercept Form and then answer the questions about the slope and the y-intercept.
### Given Equation in Standard Form:
[tex]\[ 12x - 4y = 8 \][/tex]
### Steps to convert to Slope-Intercept Form ([tex]\(y = mx + b\)[/tex]):
1. Subtract [tex]\(12x\)[/tex] from both sides to isolate the [tex]\(y\)[/tex] term on one side:
[tex]\[ -4y = -12x + 8 \][/tex]
2. Divide both sides by [tex]\(-4\)[/tex] to solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{-12x + 8}{-4} \][/tex]
3. Simplify the right-hand side:
[tex]\[ y = 3x - 2 \][/tex]
### Equation in Slope-Intercept Form:
[tex]\[ y = 3x - 2 \][/tex]
### Answering the Questions:
- The slope ([tex]\(m\)[/tex]) is:
[tex]\[ 3 \][/tex]
- The [tex]\(y\)[/tex]-intercept ([tex]\(b\)[/tex]) is:
[tex]\[ -2 \][/tex]
### Final Submission:
1. Start with the equation in Standard Form: [tex]\( 12x - 4y = 8 \)[/tex]
2. Subtract [tex]\( 12x \)[/tex] from both sides: [tex]\( -4y = -12x + 8 \)[/tex]
3. Divide both sides by [tex]\(-4\)[/tex]: [tex]\( y = 3x - 2 \)[/tex]
4. Result in Slope-Intercept Form: [tex]\( y = 3x - 2 \)[/tex]
- The slope is: [tex]\( 3 \)[/tex]
- The [tex]\( y \)[/tex]-intercept is: [tex]\( -2 \)[/tex]
Submit ✔
### Given Equation in Standard Form:
[tex]\[ 12x - 4y = 8 \][/tex]
### Steps to convert to Slope-Intercept Form ([tex]\(y = mx + b\)[/tex]):
1. Subtract [tex]\(12x\)[/tex] from both sides to isolate the [tex]\(y\)[/tex] term on one side:
[tex]\[ -4y = -12x + 8 \][/tex]
2. Divide both sides by [tex]\(-4\)[/tex] to solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{-12x + 8}{-4} \][/tex]
3. Simplify the right-hand side:
[tex]\[ y = 3x - 2 \][/tex]
### Equation in Slope-Intercept Form:
[tex]\[ y = 3x - 2 \][/tex]
### Answering the Questions:
- The slope ([tex]\(m\)[/tex]) is:
[tex]\[ 3 \][/tex]
- The [tex]\(y\)[/tex]-intercept ([tex]\(b\)[/tex]) is:
[tex]\[ -2 \][/tex]
### Final Submission:
1. Start with the equation in Standard Form: [tex]\( 12x - 4y = 8 \)[/tex]
2. Subtract [tex]\( 12x \)[/tex] from both sides: [tex]\( -4y = -12x + 8 \)[/tex]
3. Divide both sides by [tex]\(-4\)[/tex]: [tex]\( y = 3x - 2 \)[/tex]
4. Result in Slope-Intercept Form: [tex]\( y = 3x - 2 \)[/tex]
- The slope is: [tex]\( 3 \)[/tex]
- The [tex]\( y \)[/tex]-intercept is: [tex]\( -2 \)[/tex]
Submit ✔
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.