The system of equations is:

1. $y = \frac{1}{2}x + 2$
2. $y = -\frac{3}{2}x - 2$

To solve this graphically, we find the intersection point of the two lines:

Step 1: Analyze the equations

• First equation ($y = \frac{1}{2}x + 2$):

  • Slope: $\frac{1}{2}$ (rise/run = 1 up, 2 right)
  • Y-intercept: $(0, 2)$

• Second equation ($y = -\frac{3}{2}x - 2$):

  • Slope: $-\frac{3}{2}$ (fall/run = 3 down, 2 right)
  • Y-intercept: $(0, -2)$

Step 2: Graph the lines

1. Plot the y-intercepts:
   • Line 1: Start at $(0, 2)$
   • Line 2: Start at $(0, -2)$
2. Use the slopes to plot additional points:
   • Line 1: From $(0, 2)$, go up 1 unit and 2 units to the right, giving a point $(2, 3)$.
   • Line 2: From $(0, -2)$, go down 3 units and 2 units to the right, giving a point $(2, -5)$.

Step 3: Find the intersection

The two lines intersect at $x = -4$ and $y = 0$. This is verified by substitution into both equations.

Solution:

• $x = -4$
• $y = 0$

Would you like a detailed step-by-step solution or graph analysis?

Follow-up questions:

1. Can you describe how slopes influence line behavior?
2. How would the solution change if one equation was nonlinear?
3. What methods besides graphing can solve systems of equations?
4. How do you interpret "no solution" graphically?
5. Why is substitution or elimination often used instead of graphing?

Tip: Always check solutions by substituting back into both equations to ensure accuracy.