To determine the point that Harold used to write the equation [tex]\( y = 3(x - 7) \)[/tex], let's break down the given information and follow a step-by-step approach:
1. Understand the Point-Slope Form:
The point-slope form of a linear equation is [tex]\( y - y_1 = m(x - x_1) \)[/tex]. Here, [tex]\( m \)[/tex] is the slope, and [tex]\( (x_1, y_1) \)[/tex] is the point on the line.
2. Rewrite the Given Equation:
The given equation is [tex]\( y = 3(x - 7) \)[/tex]. To match this with the point-slope form, we can rewrite it as:
[tex]\[ y - 0 = 3(x - 7) \][/tex]
By comparing this with the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], we see that:
- The slope [tex]\( m \)[/tex] is 3.
- [tex]\( x_1 = 7 \)[/tex] and [tex]\( y_1 = 0 \)[/tex].
3. Identify the Point:
The point [tex]\( (x_1, y_1) \)[/tex] used in the equation is [tex]\( (7, 0) \)[/tex].
Therefore, the correct point Harold used is [tex]\( (7, 0) \)[/tex].
The correct answer is:
[tex]\[ \boxed{(7, 0)} \][/tex]
