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Let's solve the problem based on the provided information.

### Given:
- Slope \( m = 5 \)
- The line passes through the point \( (5, 4) \)

### 1. **Point-Slope Form of the Equation:**

The **point-slope form** of a line's equation is:
\[
y - y_1 = m(x - x_1)
\]
where:
- \( m \) is the slope,
- \( (x_1, y_1) \) is a point on the line.

Substitute the given values:
\[
y - 4 = 5(x - 5)
\]

This is the point-slope form of the equation.

### 2. **Slope-Intercept Form of the Equation:**

The **slope-intercept form** is:
\[
y = mx + b
\]
We can simplify the point-slope equation to convert it to this form:

\[
y - 4 = 5(x - 5)
\]
Distribute the 5:
\[
y - 4 = 5x - 25
\]
Add 4 to both sides:
\[
y = 5x - 21
\]

This is the slope-intercept form of the equation: \( y = 5x - 21 \).

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Would you like more details or explanations on any part of this? Here are some related questions you might find helpful:

1. How can you derive the point-slope form from two points?
2. What is the significance of the slope in real-life scenarios?
3. How do you convert the slope-intercept form back to point-slope form?
4. How can you find the equation of a line given two points?
5. How do parallel and perpendicular lines relate to their slopes?

**Tip:** Always remember, the point-slope form is useful when you know a point on the line and the slope, while the slope-intercept form is great for quickly graphing the line.

Write the point-slope form of the line's equation satisfying the given conditions: Slope = 5, passing through (5, 4). Then use the point-slope form to write the slope-intercept form of the equation.

Learn how to write the point-slope and slope-intercept form of a line given a slope of 5 and passing through the point (5,4). This problem demonstrates the conversion between forms of linear equations, suitable for Grades 8-10.

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