Let's take a detailed look at the point-slope form of a line. The point-slope form of a line is expressed as:
[tex]\[ y - y_1 = m (x - x_1) \][/tex]
Here:
- [tex]\( y \)[/tex] and [tex]\( x \)[/tex] are the variables representing any point on the line.
- [tex]\( y_1 \)[/tex] and [tex]\( x_1 \)[/tex] are the coordinates of a specific point on the line.
- [tex]\( m \)[/tex] is the slope of the line.
Given the structure of the point-slope form, let’s verify whether the provided statement about the point-slope form of a line is accurate.
Statement to check: The point-slope form of a line is [tex]\( y - y_1 = m (x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
Comparing this statement with the defined point-slope form:
1. Form: The statement says [tex]\( y - y_1 = m (x - x_1) \)[/tex], which matches the point-slope form definition exactly.
2. Definitions:
- [tex]\( m \)[/tex] indeed represents the slope of the line.
- [tex]\( (x_1, y_1) \)[/tex] correctly denotes a specific point through which the line passes.
Given this consistency, we can conclude the statement is indeed in alignment with the definition and properties of the point-slope form of a line. Hence, the statement is:
True.
So, the correct answer to the question:
- A. True
