Question

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

Explanation:

Step1: Recall point-slope formula

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

Step2: Substitute given values

Here, $m = \frac{2}{5}$, $x_1 = -2$, $y_1 = 4$. Substitute into the formula:
$y - 4 = \frac{2}{5}(x - (-2))$
Simplify the sign inside the parentheses:
$y - 4 = \frac{2}{5}(x + 2)$

Step3: Match with options

Compare the derived equation to the provided choices.

Answer:

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