The given equation is:

$6x + 15y = -75$

We need to convert this into slope-intercept form, which is given by:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

Step 1: Solve for $y$.

We start by isolating $y$ on one side of the equation:

$15y = -6x - 75$

Step 2: Divide by 15.

Next, divide the entire equation by 15 to simplify:

$y = \frac{-6x - 75}{15}$

Step 3: Simplify the terms.

Now simplify each term:

$y = \frac{-6}{15}x + \frac{-75}{15}$

This simplifies to:

$y = -\frac{2}{5}x - 5$

So the equation in slope-intercept form is:

$y = -\frac{2}{5}x - 5$

This means the slope ($m$) is $-\frac{2}{5}$ and the y-intercept ($b$) is $-5$.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How can you determine the slope of a line from an equation?
2. What does the slope-intercept form of a line represent geometrically?
3. How do you convert equations with fractions into slope-intercept form?
4. What is the interpretation of the y-intercept in real-life scenarios?
5. How can you graph a line using the slope and y-intercept?

Tip: Always check your final equation by plugging in values to verify that it satisfies the original equation.