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 given by \(y - y_1=m(x - x_1)\), 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 \((-2,4)\), so \(x_1=-2\) and \(y_1 = 4\). The slope \(m=\frac{2}{5}\).

Step3: Substitute into point - slope form

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

Answer:

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