To find the y-intercept of a line, you can use the point-slope form of a linear equation:
\[ y - y_1 = m(x - x_1) \]
where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line.
In this case, the slope \(m = 3\) and the point is \((-1, -7)\). Substituting these values into the equation gives:
\[ y - (-7) = 3(x - (-1)) \]
This simplifies to:
\[ y + 7 = 3(x + 1) \]
Now simplify the right side:
\[ y + 7 = 3x + 3 \]
Next, isolate \(y\):
\[ y = 3x + 3 - 7 \]
\[ y = 3x - 4 \]
From the equation \(y = 3x - 4\), we can see that the y-intercept (the value of \(y\) when \(x = 0\)) is \(-4\).
Thus, the y-intercept of the line is:
\(-4\)