which equation represents a line that passes through (-2, 4) and has a slope of $\frac{2}{5}$?\n$y…

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Identify values of $x_1$, $y_1$ and $m$

Given the point $(-2,4)$ and slope $m = \frac{2}{5}$, we have $x_1=-2$, $y_1 = 4$ and $m=\frac{2}{5}$.

Step3: Substitute values into point - slope form

Substituting into $y - y_1=m(x - x_1)$ gives $y - 4=\frac{2}{5}(x-(-2))$, which simplifies to $y - 4=\frac{2}{5}(x + 2)$.

Answer:

A. $y - 4=\frac{2}{5}(x + 2)$