To find the y-intercept of the line given in point-slope form, we first need to convert the point-slope equation to slope-intercept form (y = mx + b).
The given equation is:
\[ y - 1 = -7(x - 3) \]
First, distribute -7 on the right side:
\[ y - 1 = -7x + 21 \]
Next, add 1 to both sides to isolate \( y \):
\[ y = -7x + 21 + 1 \] \[ y = -7x + 22 \]
Now, in the slope-intercept form \( y = mx + b \), the y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the equation \( y = -7x + 22 \), we see that the y-intercept \( b \) is:
\[ b = 22 \]
Therefore, the y-intercept of the line is 22.