You provided two expressions: one in slope-intercept form and the other is an equation to be simplified. Let's clarify each:

1. First equation: $y = -3x + 4$

   • This is already in slope-intercept form, with slope $m = -3$ and y-intercept $b = 4$.

2. Second expression: $-6x - 2y + 8 = 0$

   • We can solve this equation by isolating $y$ in terms of $x$.

Step 1: Simplify the second equation

Start with: $-6x - 2y + 8 = 0$

Move $-6x$ and $8$ to the other side: $-2y = 6x - 8$

Now divide everything by $-2$: $y = -3x + 4$

Step 2: Compare the two equations

Both equations are exactly the same: $y = -3x + 4$

This means that the second equation is just a rearranged version of the first, so the two lines are actually the same line.

Conclusion:

Both equations represent the same line, meaning they are coincident (overlapping). There is no distinct system of two lines here, as both equations describe the same relationship between $x$ and $y$.

Would you like more details or have any questions?

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Here are 5 related questions to expand the topic:

1. How do you find the intersection point of two distinct linear equations?
2. What is the geometric interpretation of two coincident lines?
3. How do you graph linear equations in slope-intercept form?
4. How do you convert between standard form and slope-intercept form of a line?
5. What does it mean when two lines are parallel versus when they coincide?

Tip: When solving systems of linear equations, always compare slopes first. Identical slopes can imply parallel or coincident lines.