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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