To solve this question, let's closely examine the given point-slope form of a line to determine its correctness. The point-slope form of a line should correctly represent the relationship between a point on the line, its slope, and another point on the line.
The standard point-slope form of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Where:
- [tex]\( m \)[/tex] is the slope of the line
- [tex]\((x_1, y_1)\)[/tex] is a specific point on the line
Now, let's compare this with the form provided in the question:
[tex]\[ y + y_1 = m(x + x_1) \][/tex]
By comparing both forms, we can see some differences.
1. In the standard form, the left side of the equation has [tex]\( y - y_1 \)[/tex], while in the provided form, it has [tex]\( y + y_1 \)[/tex].
2. On the right side of the equation, the standard form has [tex]\( (x - x_1) \)[/tex], while the provided form has [tex]\( (x + x_1) \)[/tex].
These differences indicate that the provided form in the question is not consistent with the standard point-slope form of a line.
To summarize:
- The given form [tex]\( y + y_1 = m(x + x_1) \)[/tex] is incorrect.
Thus, the correct answer to the question is:
B. False
