To determine the equation of a line that passes through the point [tex]\((-2, 4)\)[/tex] and has a slope of [tex]\(\frac{2}{5}\)[/tex], we can use the point-slope form of the equation of a line, which is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here,
[tex]\( (x_1, y_1) = (-2, 4) \)[/tex] is the given point, and
[tex]\( m = \frac{2}{5} \)[/tex] is the given slope.
Plugging these values into the point-slope form gives:
[tex]\[ y - 4 = \frac{2}{5}(x - (-2)) \][/tex]
Since [tex]\( x - (-2) = x + 2 \)[/tex], the equation simplifies to:
[tex]\[ y - 4 = \frac{2}{5}(x + 2) \][/tex]
Therefore, the equation that represents the line passing through [tex]\((-2, 4)\)[/tex] with a slope of [tex]\(\frac{2}{5}\)[/tex] is:
[tex]\[ y - 4 = \frac{2}{5}(x + 2) \][/tex]
So, the correct answer is:
[tex]\[ \boxed{y - 4=\frac{2}{5}(x+2)} \][/tex]
