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).