The slope-intercept form of a linear equation is given by:

$y = mx + b$

where:

• $m$ is the slope of the line.
• $b$ is the y-intercept, which is the value of $y$ when $x = 0$.

Given:

• Slope $m = -1$
• Y-intercept $b = -7$

Substituting these values into the slope-intercept form:

$y = -1x - 7$

This simplifies to:

$y = -x - 7$

So, the slope-intercept form of the equation is $y = -x - 7$.

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. How do you find the slope of a line given two points?
2. What is the point-slope form of a linear equation?
3. How can you convert a slope-intercept equation to standard form?
4. What does the slope of a line represent in a real-world context?
5. How do you determine the x-intercept from the slope-intercept form?

Tip: Always remember that the y-intercept is where the line crosses the y-axis, so it's the point where $x = 0$.