Write the standard form of the equation of the line passing through 2,4 with slope 3/5

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.

Learn how to write the standard form of the equation of a line passing through the point (2, 4) with a slope of 3/5. This problem covers key concepts in geometry and linear equations, including the point-slope form and standard form of linear equations. Suitable for high school students.

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