Question

what is the point - slope form of the line with slope \\(\frac{2}{5}\\) that passes through the point \\((-4, -7)\\)? \\(\circ\\ y - 4 = \frac{2}{5}(x - 7)\\). \\(\circ\\ y + 4 = \frac{2}{5}(x + 7)\\) \\(\circ\\ y - 7 = \frac{2}{5}(x - 4)\\) \\(\circ\\ y + 7 = \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: Identify given values

We have $m = \frac{2}{5}$, $x_1 = -4$, $y_1 = -7$.

Step3: Substitute values into formula

Substitute into $y - y_1 = m(x - x_1)$:
$y - (-7) = \frac{2}{5}(x - (-4))$
Simplify the double negatives:
$y + 7 = \frac{2}{5}(x + 4)$

Answer:

$y + 7 = \frac{2}{5}(x + 4)$