We are given the equation:

$-6x - 2y = 5$

To find the y-intercept and slope of the line, we need to rewrite this equation in slope-intercept form, which is:

$y = mx + b$

Where:

• $m$ is the slope.
• $b$ is the y-intercept.

Let's rearrange the given equation to match this form:

Step 1: Solve for $y$

$-2y = 6x + 5$

Now, divide by $-2$ to isolate $y$: $y = -3x - \frac{5}{2}$

Step 2: Identify the slope and y-intercept

Now that the equation is in the form $y = mx + b$:

• The slope ($m$) is $-3$.
• The y-intercept ($b$) is $-\frac{5}{2}$.

Final Answers:

• y-intercept: $-\frac{5}{2}$
• Slope: $-3$

Would you like further details or have any questions about these steps? Here are some related questions to expand on this concept:

1. How do you graph a line using the slope and y-intercept?
2. What are the steps to convert an equation from standard form to slope-intercept form?
3. How would you find the x-intercept of the line?
4. Can a line have no slope? If so, what is that line called?
5. What is the significance of the slope in real-life applications?

Tip: Always check if the equation is in the correct format for identifying slope and intercepts—this makes the process much quicker.