To write the equation of a line in slope-intercept form, we can use the formula:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
We are given:
- Slope \( m = 7 \)
- A point on the line \( (-1, -8) \)
First, we can substitute the slope and the point into the equation to solve for \( b \).
Start with the equation:
\[ y = 7x + b \]
Substituting \( x = -1 \) and \( y = -8 \):
\[ -8 = 7(-1) + b \]
Calculating the right-hand side:
\[ -8 = -7 + b \]
Now, we add 7 to both sides to solve for \( b \):
\[ -8 + 7 = b \] \[ b = -1 \]
Now that we have \( b \), we can write the equation of the line:
\[ y = 7x - 1 \]
Thus, the equation of the line in slope-intercept form is:
\[ \boxed{y = 7x - 1} \]