Absolutely! Let's work through the question step-by-step.
We know that the line has a slope ([tex]\( m \)[/tex]) of 4 and it passes through the point [tex]\((-2, 5)\)[/tex].
The point-slope form of the equation of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here:
- [tex]\( m = 4 \)[/tex]
- [tex]\( (x_1, y_1) = (-2, 5) \)[/tex]
We substitute these values into the point-slope form equation:
[tex]\[ y - 5 = 4(x - (-2)) \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ y - 5 = 4(x + 2) \][/tex]
Therefore, the equation of the line in point-slope form is:
[tex]\[ \boxed{y - 5 = 4(x + 2)} \][/tex]
The correct option is:
A. [tex]\( y - 5 = 4(x + 2) \)[/tex]
