To determine the point-slope form of the line with a given slope and passing through a given point, we use the point-slope form equation of a line:
[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 point on the line
Given:
- The slope [tex]\( m = -3 \)[/tex]
- The point [tex]\((x_1, y_1) = (10, -1)\)[/tex]
Substituting these values into the point-slope form equation:
[tex]\[ y - (-1) = -3(x - 10) \][/tex]
This simplifies to:
[tex]\[ y + 1 = -3(x - 10) \][/tex]
Thus, the point-slope form of the line with a slope of -3 passing through the point (10, -1) is:
[tex]\[ y + 1 = -3(x - 10) \][/tex]
Comparing this with the given options:
- A. [tex]\( y+1=3(x-10) \)[/tex]
- B. [tex]\( y+1=-3(x-10) \)[/tex]
- C. [tex]\( y+1=3(x+10) \)[/tex]
- D. [tex]\( x+1=-3(y-10) \)[/tex]
The correct answer is:
[tex]\[ \boxed{B} \][/tex]
