To determine the point-slope form of the equation of a line with a given slope and point, we use the point-slope formula. The point-slope form of the equation of a line is defined as:
[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:
- Slope ([tex]\( m \)[/tex]) is 6
- The line passes through the point [tex]\((1, 2)\)[/tex]
We substitute the given point and slope into the point-slope formula:
[tex]\[ y - 2 = 6(x - 1) \][/tex]
Thus, the correct form of the equation is:
[tex]\[ y - 2 = 6(x - 1) \][/tex]
Comparing this with the answer choices:
A. [tex]\( x + 1 = 6(y + 2) \)[/tex] - This form is not correct.
B. [tex]\( y - 2 = 6(x - 1) \)[/tex] - This form matches our equation.
C. [tex]\( y + 2 = 6(x - 1) \)[/tex] - This form does not match.
D. [tex]\( y + 2 = 6(x + 1) \)[/tex] - This form does not match.
Therefore, the correct answer is:
B. [tex]\( y - 2 = 6(x - 1) \)[/tex]
