To find the slope and $y$-intercept of the equation $-2x + y = 3$, let's rewrite it in the slope-intercept form, which is $y = mx + c$, where $m$ is the slope and $c$ is the $y$-intercept.

Starting with: $-2x + y = 3$

Add $2x$ to both sides to isolate $y$: $y = 2x + 3$

Now, in this form, we can see that:

• The slope $m = 2$
• The $y$-intercept $c = 3$

So, the correct answer is option (b): $m = 2, c = 3$.

Would you like more details or have any questions?

Here are some related questions to consider:

1. How do you convert an equation to slope-intercept form?
2. What is the significance of the slope in a linear equation?
3. How can you find the $y$-intercept from different forms of linear equations?
4. How do the slope and $y$-intercept influence the graph of a line?
5. What are some common methods to find the slope of a line given two points?

Tip: Always try to rewrite linear equations in slope-intercept form to easily identify the slope and $y$-intercept.