Let's begin by solving the equation $2x + 3y = 6$ for $y$ in terms of $x$ to make it easier to plot.

Step 1: Solve for $y$

$2x + 3y = 6$ Subtract $2x$ from both sides: $3y = -2x + 6$ Now, divide by 3 to isolate $y$: $y = -\frac{2}{3}x + 2$

Step 2: Choose values for $x$ to find corresponding $y$-values

Let's choose two values of $x$ to find their corresponding $y$-values.

For $x = 0$:

$y = -\frac{2}{3}(0) + 2 = 2$ So, one point is $(0, 2)$.

For $x = 3$:

$y = -\frac{2}{3}(3) + 2 = -2 + 2 = 0$ So, another point is $(3, 0)$.

Step 3: Plot the points and graph the line

• The points $(0, 2)$ and $(3, 0)$ are on the line.
• Draw a line connecting these two points.

Let me know if you'd like to see a visual of the graph!

Here are 5 related questions:

1. How do you find the slope of a line given its equation?
2. What does the slope of this line represent in terms of the relationship between $x$ and $y$?
3. How do you graph a line using the slope-intercept form $y = mx + b$?
4. How do you find the x-intercept and y-intercept of a linear equation?
5. Can you convert this equation into standard form from slope-intercept form?

Tip:

The slope-intercept form of a line $y = mx + b$ is very helpful because it directly shows the slope ($m$) and the y-intercept ($b$), which are easy to plot on the graph.