To find the equation of the line passing through the points $(3, 0)$ and $(0, 2)$, we follow these steps:

1. Find the slope of the line:

The slope $m$ is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates $(x_1, y_1) = (3, 0)$ and $(x_2, y_2) = (0, 2)$:

$m = \frac{2 - 0}{0 - 3} = \frac{2}{-3} = -\frac{2}{3}$

2. Use the point-slope form of the equation:

The point-slope form of a line is:

$y - y_1 = m(x - x_1)$

Using the point $(3, 0)$ and the slope $m = -\frac{2}{3}$:

$y - 0 = -\frac{2}{3}(x - 3)$

$y = -\frac{2}{3}(x - 3)$

3. Simplify the equation:

Distribute the slope:

$y = -\frac{2}{3}x + 2$

4. Convert to standard form:

To convert to standard form $Ax + By = C$, eliminate the fraction by multiplying the entire equation by 3:

$3y = -2x + 6$

Rearrange terms to get the standard form:

$2x + 3y = 6$

Thus, the equation of the line in standard form is:

$\boxed{2x + 3y = 6}$

Would you like any further details or explanations?

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Here are 5 related questions to explore:

1. What is the slope-intercept form of a line?
2. How do you find the slope given two points?
3. What is the meaning of the slope in real-world applications?
4. Can a vertical line be expressed in standard form?
5. How do you convert from point-slope form to slope-intercept form?

Tip: The standard form of a linear equation is useful when you need to find intercepts quickly.