through: $$ (-5,3) $$, parallel to $$ y=\frac{2}{5} x+2 $$

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To find the equation of a line that **passes through the point $$(-5, 3)$$** and is **parallel** to the line $$y = \frac{2}{5}x + 2$$, follow these steps:

### 1. Understand Parallel Lines
Parallel lines have the **same slope**. The given line is:

$$
y = \frac{2}{5}x + 2
$$

Here, the **slope ($$m$$)** is $$\frac{2}{5}$$.

### 2. Use the Point-Slope Form
The **point-slope form** of a line is:

$$
y - y_1 = m(x - x_1)
$$

Where:
- $$m$$ is the slope.
- $$(x_1, y_1)$$ is a point on the line.

Given:
- Slope $$m = \frac{2}{5}$$
- Point $$(x_1, y_1) = (-5, 3)$$

Plug these values into the point-slope form:

$$
y - 3 = \frac{2}{5}(x - (-5))
$$
$$
y - 3 = \frac{2}{5}(x + 5)
$$

### 3. Simplify to Slope-Intercept Form
To express the equation in the slope-intercept form ($$y = mx + b$$):

$$
y - 3 = \frac{2}{5}x + \frac{2}{5} \times 5
$$
$$
y - 3 = \frac{2}{5}x + 2
$$
$$
y = \frac{2}{5}x + 2 + 3
$$
$$
y = \frac{2}{5}x + 5
$$

### **Final Equation**
$$
\boxed{y = \frac{2}{5}x + 5}
$$

This is the equation of the line that passes through $$(-5, 3)$$ and is parallel to $$y = \frac{2}{5}x + 2$$.
The equation of the line is $$ y = \frac{2}{5}x + 5 $$.

through: \( (-5,3) \), parallel to \( y=\frac{2}{5} x+2 \)

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