To find the equation of a line in point-slope form given the slope and a point on the line, you can use the point-slope 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 the given point on the line.
In this case, the slope ([tex]\( m \)[/tex]) is 4 and the point ([tex]\( x_1, y_1 \)[/tex]) is [tex]\((-2, 5)\)[/tex].
Let's substitute the values into the point-slope formula:
[tex]\[ y - 5 = 4(x - (-2)) \][/tex]
Simplify the equation:
[tex]\[ y - 5 = 4(x + 2) \][/tex]
Thus, the equation of the line in point-slope form is:
[tex]\[ y - 5 = 4(x + 2) \][/tex]
By comparing this with the given options:
- A. [tex]\( y + 2 = 4(x - 5) \)[/tex]
- B. [tex]\( y - 5 = 4(x + 2) \)[/tex]
- C. [tex]\( y + 5 = 4(x - 2) \)[/tex]
- D. [tex]\( y - 5 = 4(x - 2) \)[/tex]
We see that the correct answer is:
B. [tex]\( y - 5 = 4(x + 2) \)[/tex]
Therefore, the correct option is B.
