To determine the point-slope form of a line with a given slope and point, we use the point-slope formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope.
Given:
- Slope ([tex]\( m \)[/tex]) = -3
- Point ([tex]\( x_1, y_1 \)[/tex]) = (10, -1)
Plug these values into the point-slope formula:
[tex]\[ y - (-1) = -3(x - 10) \][/tex]
Simplify the equation:
[tex]\[ y + 1 = -3(x - 10) \][/tex]
Hence, the point-slope form of the line is:
[tex]\[ y + 1 = -3(x - 10) \][/tex]
So, the correct answer is:
D. [tex]\( y + 1 = -3(x - 10) \)[/tex]
