The equation given is:

$y = -2x - 5$

This represents a linear equation in slope-intercept form:

$y = mx + b$

where:

• $m = -2$ (the slope)
• $b = -5$ (the y-intercept)

Key Properties:

1. Slope: $-2$ means the line decreases by 2 units for every 1 unit increase in $x$.
2. Y-Intercept: The graph crosses the $y$-axis at $(0, -5)$.
3. X-Intercept: Setting $y = 0$ to find where the graph crosses the $x$-axis: $0 = -2x - 5$ $2x = -5$ $x = -\frac{5}{2}$ So, the x-intercept is $\left(-\frac{5}{2}, 0\right)$.
4. Graph Behavior: The line slopes downward from left to right due to the negative slope.
5. Parallel and Perpendicular Lines:
   • Any line with the same slope ($m = -2$) is parallel.
   • A perpendicular line will have a slope of $\frac{1}{2}$ (the negative reciprocal of $-2$).

Would you like a graph or further clarification?

Related Questions:

1. What is the equation of a line parallel to $y = -2x - 5$ passing through $(3,4)$?
2. How do you convert this equation into standard form $Ax + By = C$?
3. What is the equation of a line perpendicular to $y = -2x - 5$ passing through $(-1,2)$?
4. How do you determine the distance from a point (e.g., $(1,1)$) to this line?
5. How does changing the slope affect the steepness of the line?

Tip:

For any linear equation in the form $y = mx + b$, the slope determines the direction and steepness, while the y-intercept tells you where the line crosses the y-axis.