To solve this system of equations by graphing, we first need to graph both lines and find the point of intersection. The two equations are:

1. $y = -2x - 4$
2. $y = -\frac{1}{2}x + 2$

Step 1: Graph the first equation $y = -2x - 4$

This is a linear equation in slope-intercept form $y = mx + b$, where:

• Slope $m = -2$
• Y-intercept $b = -4$

To plot this:

• Start at $(0, -4)$ for the y-intercept.
• From there, move down 2 units and to the right 1 unit (since the slope is -2), giving you the next point.
• Plot a few more points if needed, and then draw the line.

Step 2: Graph the second equation $y = -\frac{1}{2}x + 2$

This is also in slope-intercept form:

• Slope $m = -\frac{1}{2}$
• Y-intercept $b = 2$

To plot this:

• Start at $(0, 2)$ for the y-intercept.
• From there, move down 1 unit and to the right 2 units (since the slope is $-\frac{1}{2}$).
• Plot a few points and draw the line.

Step 3: Find the intersection point

Graphically, the point where the two lines intersect is the solution to the system of equations. After plotting both lines, you will see that the lines intersect at $(2, -8)$.

Final Answer:

The solution to the system of equations is $x = 2$ and $y = -8$, or the point $(2, -8)$.

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

1. How do you determine the slope and y-intercept from an equation in slope-intercept form?
2. What is the significance of the point where two lines intersect?
3. Can all systems of linear equations be solved graphically?
4. How can you check your solution algebraically after graphing?
5. What does it mean if two lines on a graph are parallel or coincide?

Tip: When graphing lines, always double-check your slope by verifying two plotted points.