The problem provided asks to rewrite the equation in slope-intercept form and identify the slope and $y$-intercept.

The given equation is: $-10x - 5y = 15$

Steps to rewrite the equation in slope-intercept form:

1. Isolate the $y$-term: $-5y = 10x + 15$ (Moved $-10x$ to the other side)

2. Solve for $y$ by dividing every term by $-5$: $y = \frac{10x}{-5} + \frac{15}{-5}$ Simplify the fractions: $y = -2x - 3$

Now, the equation is in slope-intercept form $y = mx + b$, where:

• The slope $m = -2$,
• The y-intercept $b = -3$.

Final Answer:

• The equation in slope-intercept form is: $y = -2x - 3$.
• The slope $m = -2$.
• The $y$-intercept is $-3$.

Do you want more details or have any further questions?

Here are 5 related questions you might consider:

1. How would you convert any linear equation into slope-intercept form?
2. What does the slope of a line represent geometrically?
3. How can you find the equation of a line given the slope and a point on the line?
4. What is the process for finding the intersection of two lines?
5. How can you graph a line using only the slope and $y$-intercept?

Tip: Remember that in slope-intercept form, $m$ (slope) indicates the steepness and direction of the line, while $b$ (the $y$-intercept) indicates where the line crosses the $y$-axis.