The given equation is \( y = 4x - 5 \), which represents a linear equation in slope-intercept form: 

\[
y = mx + b
\]

where:
- \( m = 4 \) is the slope, which means for every increase of 1 unit in \( x \), \( y \) increases by 4 units.
- \( b = -5 \) is the y-intercept, which is the point where the line crosses the y-axis (\( x = 0 \)).

### Key properties:
1. **Slope**: The slope \( m = 4 \) shows that the line is increasing and relatively steep.
2. **Y-intercept**: When \( x = 0 \), \( y = -5 \), so the line crosses the y-axis at \( (0, -5) \).
3. **X-intercept**: Setting \( y = 0 \) and solving for \( x \):
   \[
   0 = 4x - 5 \quad \Rightarrow \quad 4x = 5 \quad \Rightarrow \quad x = \frac{5}{4} = 1.25
   \]
   So, the line crosses the x-axis at \( \left( \frac{5}{4}, 0 \right) \).

Would you like further details or have any questions?

Here are some related questions for exploration:
1. What would happen if the slope \( m \) were negative?
2. How do you find the distance between two points on this line?
3. What is the equation of a parallel line to \( y = 4x - 5 \)?
4. How can you rewrite the equation in standard form \( Ax + By = C \)?
5. What would the graph look like if \( y = 4x + 2 \)?

**Tip:** For any linear equation, the slope determines the line's direction (positive slope = increasing line, negative slope = decreasing line).

Explore how to solve and analyze the linear equation y = 4x - 5. This problem covers essential algebraic concepts like slope-intercept form, x-intercepts, and y-intercepts, making it perfect for students in Grades 7-9. Learn how to find key points on the graph and understand how the slope affects the line's direction.

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