The image shows a system of two linear equations that need to be graphed and solved. The equations are:

1. $y = -2x + 4$
2. $y = 6x - 4$

To solve these equations graphically:

1. Plot the first equation $y = -2x + 4$:

   • The y-intercept is $4$ (point $(0, 4)$).
   • The slope is $-2$, so from $(0, 4)$, move down 2 units and 1 unit to the right to get another point $(1, 2)$.

2. Plot the second equation $y = 6x - 4$:

   • The y-intercept is $-4$ (point $(0, -4)$).
   • The slope is $6$, so from $(0, -4)$, move up 6 units and 1 unit to the right to get another point $(1, 2)$.

3. Find the intersection of the two lines:

   • The lines intersect at $(1, 2)$. This is the solution to the system of equations.

Would you like me to show this in a graph or explain further? Let me know!

Here are some follow-up questions for exploration:

1. What is the importance of the slope in graphing linear equations?
2. How can you confirm the solution algebraically?
3. Can these equations represent a real-world scenario? Provide an example.
4. What happens if two lines in a system are parallel?
5. How would you solve these equations using substitution or elimination?

Tip: Always check the intersection point in both equations to confirm accuracy!