To find the equation of a line in point-slope form, you will need two things: the slope of the line and a point that the line passes through. The point-slope form of a line is given by the formula:
[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 that the line passes through.
We are given:
- The slope [tex]\(m = 3\)[/tex],
- The point [tex]\((x_1, y_1) = (2, 1)\)[/tex].
Plug these values into the point-slope form equation:
[tex]\[ y - 1 = 3(x - 2) \][/tex]
So, the point-slope form of the line with slope 3 that passes through the point [tex]\((2, 1)\)[/tex] is:
[tex]\[ y - 1 = 3(x - 2) \][/tex]
Comparing this with the provided options:
A. [tex]\( y-1=3(x-2) \)[/tex]
B. [tex]\( y-2=3(x+1) \)[/tex]
C. [tex]\( y+1=3(x+2) \)[/tex]
D. [tex]\( y-2=3(x-1) \)[/tex]
The correct answer is option A:
[tex]\[ y-1=3(x-2) \][/tex]
Thus, the correct answer is A.
