Explore IDNLearn.com's extensive Q&A database and find the answers you're looking for. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.
Sagot :
To determine which graph represents the equation [tex]\( y + 2 = 3(x - 1) \)[/tex], we need to convert this equation into slope-intercept form, which is [tex]\( y = mx + b \)[/tex]. Here are the steps to convert and analyze the equation:
1. Start with the given equation:
[tex]\[ y + 2 = 3(x - 1) \][/tex]
2. Distribute the 3 on the right side:
[tex]\[ y + 2 = 3x - 3 \][/tex]
3. Isolate [tex]\( y \)[/tex] by subtracting 2 from both sides:
[tex]\[ y = 3x - 3 - 2 \][/tex]
4. Simplify the right-hand side:
[tex]\[ y = 3x - 5 \][/tex]
So, the equation in slope-intercept form is [tex]\( y = 3x - 5 \)[/tex].
Now, we can interpret this equation:
- The slope ([tex]\(m\)[/tex]) is 3, which means the line rises 3 units vertically for every 1 unit it moves horizontally.
- The y-intercept ([tex]\(b\)[/tex]) is -5, which means the line crosses the y-axis at [tex]\( (0, -5) \)[/tex].
The correct graph will be the one that has a slope of 3 and crosses the y-axis at -5.
So, the graph that represents the equation [tex]\( y = 3x - 5 \)[/tex] is the correct answer.
1. Start with the given equation:
[tex]\[ y + 2 = 3(x - 1) \][/tex]
2. Distribute the 3 on the right side:
[tex]\[ y + 2 = 3x - 3 \][/tex]
3. Isolate [tex]\( y \)[/tex] by subtracting 2 from both sides:
[tex]\[ y = 3x - 3 - 2 \][/tex]
4. Simplify the right-hand side:
[tex]\[ y = 3x - 5 \][/tex]
So, the equation in slope-intercept form is [tex]\( y = 3x - 5 \)[/tex].
Now, we can interpret this equation:
- The slope ([tex]\(m\)[/tex]) is 3, which means the line rises 3 units vertically for every 1 unit it moves horizontally.
- The y-intercept ([tex]\(b\)[/tex]) is -5, which means the line crosses the y-axis at [tex]\( (0, -5) \)[/tex].
The correct graph will be the one that has a slope of 3 and crosses the y-axis at -5.
So, the graph that represents the equation [tex]\( y = 3x - 5 \)[/tex] is the correct answer.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.