To determine which point Harold used to write the equation [tex]\( y = 3(x - 7) \)[/tex] using the point-slope form, we start by recalling the point-slope form of a linear equation:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
In this form:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( (x_1, y_1) \)[/tex] is a specific point on the line.
Given the equation [tex]\( y = 3(x - 7) \)[/tex], let's compare this with the point-slope form:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
From the equation, we can observe:
- The slope [tex]\( m \)[/tex] is [tex]\( 3 \)[/tex].
- The term [tex]\( x - 7 \)[/tex] implies that [tex]\( x_1 \)[/tex] is [tex]\( 7 \)[/tex].
Now, since [tex]\( y \)[/tex] on the left-hand side is not subtracted by anything, it implies that [tex]\( y_1 \)[/tex] is [tex]\( 0 \)[/tex] (because [tex]\( y - 0 \)[/tex] is just [tex]\( y \)[/tex]).
Thus, the point [tex]\( (x_1, y_1) \)[/tex] that Harold used is:
[tex]\[ (7, 0) \][/tex]
Therefore, the correct point is:
[tex]\[ (7, 0) \][/tex]
### Conclusion:
Harold used the point [tex]\((7, 0)\)[/tex]. Hence, the correct answer is:
[tex]\[ \boxed{(7,0)} \][/tex]
