Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Sure! Let's use the slope-intercept form to graph the given equation [tex]\(3x + 2y = 6\)[/tex].
### Step-by-Step Solution:
1. Understand the Given Equation:
The equation provided is in standard form: [tex]\(3x + 2y = 6\)[/tex].
2. Convert to the Slope-Intercept Form:
To convert the equation to the slope-intercept form, which is [tex]\(y = mx + b\)[/tex] where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept, we need to solve for [tex]\(y\)[/tex]:
[tex]\[ 3x + 2y = 6 \][/tex]
First, isolate [tex]\(2y\)[/tex] on one side of the equation:
[tex]\[ 2y = -3x + 6 \][/tex]
Next, divide every term by 2:
[tex]\[ y = \frac{-3}{2}x + 3 \][/tex]
3. Identify the Slope and Y-Intercept:
From the slope-intercept form [tex]\(y = \frac{-3}{2}x + 3\)[/tex], we identify:
- The slope ([tex]\(m\)[/tex]) is [tex]\(-\frac{3}{2}\)[/tex].
- The y-intercept ([tex]\(b\)[/tex]) is 3.
4. Graphing the Equation:
- Plot the Y-Intercept: Start by plotting the y-intercept on the graph. Since [tex]\(b = 3\)[/tex], place a point at [tex]\((0, 3)\)[/tex] on the y-axis.
- Use the Slope to Find Another Point: The slope is [tex]\(-\frac{3}{2}\)[/tex], which means for every 2 units you move to the right (positive direction of the x-axis), you move 3 units down (negative direction of the y-axis).
From the y-intercept point [tex]\((0, 3)\)[/tex]:
- Move 2 units to the right to [tex]\((2, 3)\)[/tex].
- Then move 3 units down to [tex]\((2, 0)\)[/tex].
- Draw the Line: With the points [tex]\((0, 3)\)[/tex] and [tex]\((2, 0)\)[/tex] plotted, draw a straight line through these points to represent the equation [tex]\(y = \frac{-3}{2}x + 3\)[/tex].
### Conclusion
To sum up, the graph of the equation [tex]\(3x + 2y = 6\)[/tex] is a straight line that crosses the y-axis at 3 (the y-intercept) and has a slope of [tex]\(-\frac{3}{2}\)[/tex].
### Step-by-Step Solution:
1. Understand the Given Equation:
The equation provided is in standard form: [tex]\(3x + 2y = 6\)[/tex].
2. Convert to the Slope-Intercept Form:
To convert the equation to the slope-intercept form, which is [tex]\(y = mx + b\)[/tex] where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept, we need to solve for [tex]\(y\)[/tex]:
[tex]\[ 3x + 2y = 6 \][/tex]
First, isolate [tex]\(2y\)[/tex] on one side of the equation:
[tex]\[ 2y = -3x + 6 \][/tex]
Next, divide every term by 2:
[tex]\[ y = \frac{-3}{2}x + 3 \][/tex]
3. Identify the Slope and Y-Intercept:
From the slope-intercept form [tex]\(y = \frac{-3}{2}x + 3\)[/tex], we identify:
- The slope ([tex]\(m\)[/tex]) is [tex]\(-\frac{3}{2}\)[/tex].
- The y-intercept ([tex]\(b\)[/tex]) is 3.
4. Graphing the Equation:
- Plot the Y-Intercept: Start by plotting the y-intercept on the graph. Since [tex]\(b = 3\)[/tex], place a point at [tex]\((0, 3)\)[/tex] on the y-axis.
- Use the Slope to Find Another Point: The slope is [tex]\(-\frac{3}{2}\)[/tex], which means for every 2 units you move to the right (positive direction of the x-axis), you move 3 units down (negative direction of the y-axis).
From the y-intercept point [tex]\((0, 3)\)[/tex]:
- Move 2 units to the right to [tex]\((2, 3)\)[/tex].
- Then move 3 units down to [tex]\((2, 0)\)[/tex].
- Draw the Line: With the points [tex]\((0, 3)\)[/tex] and [tex]\((2, 0)\)[/tex] plotted, draw a straight line through these points to represent the equation [tex]\(y = \frac{-3}{2}x + 3\)[/tex].
### Conclusion
To sum up, the graph of the equation [tex]\(3x + 2y = 6\)[/tex] is a straight line that crosses the y-axis at 3 (the y-intercept) and has a slope of [tex]\(-\frac{3}{2}\)[/tex].
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.