To write the standard form of the equation of a line passing through the point $(2, 4)$ with a slope of $\frac{3}{5}$, follow these steps:

Step 1: Start with the point-slope form

The point-slope form of the equation of a line is:

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

where $(x_1, y_1)$ is the given point and $m$ is the slope. Here, $(x_1, y_1) = (2, 4)$ and $m = \frac{3}{5}$.

Substituting the values:

$y - 4 = \frac{3}{5}(x - 2)$

Step 2: Distribute and simplify

Distribute the $\frac{3}{5}$:

$y - 4 = \frac{3}{5}x - \frac{6}{5}$

Add 4 to both sides:

$y = \frac{3}{5}x - \frac{6}{5} + 4$

Convert 4 to a fraction with a denominator of 5:

$y = \frac{3}{5}x - \frac{6}{5} + \frac{20}{5}$

Combine the fractions:

$y = \frac{3}{5}x + \frac{14}{5}$

Step 3: Convert to standard form

The standard form of a line is $Ax + By = C$, where $A$, $B$, and $C$ are integers. To convert the equation to this form, first eliminate the fractions by multiplying everything by 5:

$5y = 3x + 14$

Now rearrange the equation to get all terms on one side:

$3x - 5y = -14$

This is the standard form of the equation of the line:

$3x - 5y = -14$

Would you like further details or have any questions?

Here are 5 related questions:

1. How would the equation change if the slope was negative?
2. What would be the equation if the line passed through a different point with the same slope?
3. How do you find the slope of a line given two points?
4. What is the general process to convert any linear equation to standard form?
5. How can you graph a line given in standard form?

Tip: When converting a linear equation to standard form, ensure that the coefficient of $x$ is positive and all coefficients are integers.