At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Use the slope-intercept form to graph the equation.

[tex]\[ 3x + 2y = 6 \][/tex]

A.
B.
C.
D.


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].
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.