Question

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

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 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)