The question asks to graph the system of equations:

1. $y = -2x - 1$
2. $y = x + 5$

Steps to Solve:

1. Graph the first equation ($y = -2x - 1$):

   • Y-intercept: The equation is in slope-intercept form ($y = mx + b$), where $b$ is the y-intercept. Here, $b = -1$, so the graph passes through $(0, -1)$.
   • Slope: The slope ($m$) is $-2$, meaning for every 1 unit increase in $x$, $y$ decreases by 2 units. Another point can be calculated as follows:
     • Starting at $(0, -1)$: Increase $x$ by 1 → $x = 1$, $y = -2(1) - 1 = -3$.
   • Points: $(0, -1)$, $(1, -3)$.

2. Graph the second equation ($y = x + 5$):

   • Y-intercept: Here, $b = 5$, so the graph passes through $(0, 5)$.
   • Slope: The slope ($m$) is $1$, meaning for every 1 unit increase in $x$, $y$ also increases by 1. Another point can be calculated:
     • Starting at $(0, 5)$: Increase $x$ by 1 → $x = 1$, $y = 1(1) + 5 = 6$.
   • Points: $(0, 5)$, $(1, 6)$.

3. Find the Intersection Point:

   • Solve the equations simultaneously: $-2x - 1 = x + 5$ Combine like terms: $-3x = 6$ Solve for $x$: $x = -2$ Substitute $x = -2$ into one of the equations, say $y = x + 5$: $y = -2 + 5 = 3$ Intersection point: $(-2, 3)$.

4. Conclusion:

   • The graphs intersect at $(-2, 3)$, which is the solution to the system of equations.

Let me know if you would like a visual graph of this system or further clarification!

Related Questions:

1. How can you verify that $(-2, 3)$ satisfies both equations?
2. What happens if the slopes of the two lines are equal?
3. How can you determine the solution without graphing?
4. How does changing the slope or y-intercept affect the graph of a line?
5. What are other methods for solving systems of linear equations?

Tip: Always label the axes and use a ruler for accuracy when graphing linear equations!