To graph the equation \(2x + 3y = 6\), follow these steps:

### Step 1: Write the equation in slope-intercept form
First, solve the equation for \(y\) in terms of \(x\).

\[
2x + 3y = 6
\]

Subtract \(2x\) from both sides:

\[
3y = -2x + 6
\]

Now, divide every term by 3 to solve for \(y\):

\[
y = -\frac{2}{3}x + 2
\]

### Step 2: Identify the slope and y-intercept
From the slope-intercept form \(y = mx + b\), we can identify:
- The slope \(m = -\frac{2}{3}\)
- The y-intercept \(b = 2\)

### Step 3: Plot the y-intercept
Start by plotting the y-intercept \((0, 2)\) on the graph.

### Step 4: Use the slope to find another point
The slope \(-\frac{2}{3}\) means that for every 3 units you move to the right (positive direction on the x-axis), you move 2 units down (negative direction on the y-axis). Starting from the y-intercept \((0, 2)\):

- Move 3 units to the right to \((3, 2)\).
- Move 2 units down to \((3, 0)\).

So, another point on the line is \((3, 0)\).

### Step 5: Draw the line
Plot the points \((0, 2)\) and \((3, 0)\) on the graph, and then draw a straight line through these points.

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Learn how to graph the linear equation 2x + 3y = 6 with a step-by-step guide. This problem involves converting the equation to slope-intercept form, identifying the slope and y-intercept, plotting points, and drawing the line. Suitable for students in Grades 7-9.

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