Write the equation of the line passing through the points $$ (4,6) $$ and $$ (-6,-2) $$

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To find the equation of the line passing through the points $$(4, 6)$$ and $$(-6, -2)$$, follow these steps:

### 1. Find the Slope ($$m$$)
The slope of a line passing through two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Plugging in the given points:

$$
m = \frac{-2 - 6}{-6 - 4} = \frac{-8}{-10} = \frac{4}{5}
$$

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

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

Using the point $$(4, 6)$$ and the slope $$m = \frac{4}{5}$$:

$$
y - 6 = \frac{4}{5}(x - 4)
$$

### 3. Simplify to Slope-Intercept Form
Let's simplify the equation to the slope-intercept form ($$y = mx + b$$):

$$
y - 6 = \frac{4}{5}x - \frac{16}{5}
$$

$$
y = \frac{4}{5}x - \frac{16}{5} + 6
$$

$$
y = \frac{4}{5}x - \frac{16}{5} + \frac{30}{5}
$$

$$
y = \frac{4}{5}x + \frac{14}{5}
$$

### Final Equation
The equation of the line in slope-intercept form is:

$$
\boxed{y = \frac{4}{5}x + \frac{14}{5}}
$$

Alternatively, you can express it in **standard form** $$Ax + By = C$$ by eliminating the fractions:

$$
5y = 4x + 14
$$

$$
4x - 5y = -14
$$

So, another valid form of the equation is:

$$
\boxed{4x - 5y = -14}
$$

Both forms accurately represent the line passing through the points $$(4, 6)$$ and $$(-6, -2)$$.
The equation of the line passing through the points $$(4, 6)$$ and $$(-6, -2)$$ is $$ y = \frac{4}{5}x + \frac{14}{5} $$.

Write the equation of the line passing through the points and

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