Question

which equation represents a line that passes through (-2, 4) and has a slope of \\(\frac{2}{5}\\)?
\\(\circ\\) \\(y - 4 = \frac{2}{5}(x + 2)\\)
\\(\circ\\) \\(y + 4 = \frac{2}{5}(x - 2)\\)
\\(\circ\\) \\(y + 2 = \frac{2}{5}(x - 4)\\)
\\(\circ\\) \\(y - 2 = \frac{2}{5}(x + 4)\\)

Explanation:

Step1: Recall Point - Slope Form

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

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

We are given that the line passes through the point $(-2,4)$ and has a slope $m = \frac{2}{5}$. So, $x_1=-2$ and $y_1 = 4$.

Step3: Substitute into Point - Slope Form

Substitute $x_1=-2$, $y_1 = 4$ and $m=\frac{2}{5}$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y - 4=\frac{2}{5}(x-(-2))$, which simplifies to $y - 4=\frac{2}{5}(x + 2)$.

Answer:

$y - 4=\frac{2}{5}(x + 2)$ (the first option)