To determine the point-slope form of a line that has a given slope and passes through a specific point, we use the point-slope formula of a linear equation, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope of the line.
In this problem, we are given:
- The slope [tex]\( m = 3 \)[/tex]
- The point [tex]\( (x_1, y_1) = (2, 1) \)[/tex]
We substitute these values into the point-slope formula:
[tex]\[ y - 1 = 3(x - 2) \][/tex]
Therefore, the point-slope form of the line with slope [tex]\(3\)[/tex] that passes through the point [tex]\((2, 1)\)[/tex] is:
[tex]\[ y - 1 = 3(x - 2) \][/tex]
So, the correct answer is not [tex]\( y - 2 = 3(x - 1) \)[/tex], rather it is [tex]\( y - 1 = 3(x - 2) \)[/tex].
Thus, the provided answer "A. [tex]\( y - 2 = 3(x - 1) \)[/tex]" is incorrect. The correct point-slope form of the line is:
[tex]\[ y - 1 = 3(x - 2) \][/tex]
