ind the equation (in terms of $$ x $$ ) of the line through the points $$ (-2,5) $$ and $$ (4,-13) $$

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To find the equation of the line through the points $$ (-2, 5) $$ and $$ (4, -13) $$, we will follow these steps:

1. **Calculate the slope (m)** of the line using the formula:
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$
   where $$ (x_1, y_1) = (-2, 5) $$ and $$ (x_2, y_2) = (4, -13) $$.

2. **Use the point-slope form** of the equation of a line:
   $$
   y - y_1 = m(x - x_1)
   $$
   We can choose either of the two points for $$ (x_1, y_1) $$.

3. **Rearrange the equation** to the slope-intercept form $$ y = mx + b $$ or standard form $$ Ax + By = C $$.

Let's start by calculating the slope $$ m $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(-13-5\right)}{\left(4-\left(-2\right)\right)}$$
- step1: Remove the parentheses:
  $$\frac{-13-5}{4-\left(-2\right)}$$
- step2: Remove the parentheses:
  $$\frac{-13-5}{4+2}$$
- step3: Subtract the numbers:
  $$\frac{-18}{4+2}$$
- step4: Add the numbers:
  $$\frac{-18}{6}$$
- step5: Reduce the numbers:
  $$\frac{-3}{1}$$
- step6: Calculate:
  $$-3$$
The slope $$ m $$ of the line is $$ -3 $$.

Now, we can use the point-slope form of the equation with one of the points, say $$ (-2, 5) $$:

$$
y - 5 = -3(x - (-2))
$$

This simplifies to:

$$
y - 5 = -3(x + 2)
$$

Next, let's rearrange this equation to find the equation in terms of $$ x $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$y-5=-3\left(x+2\right)$$
- step1: Rewrite the expression:
  $$y-5=-3x-6$$
- step2: Move the constant to the right side:
  $$y=-3x-6+5$$
- step3: Add the numbers:
  $$y=-3x-1$$
The equation of the line in terms of $$ x $$ is:

$$
y = -3x - 1
$$

This is the slope-intercept form of the equation of the line that passes through the points $$ (-2, 5) $$ and $$ (4, -13) $$.
The equation of the line is $$ y = -3x - 1 $$.

ind the equation (in terms of ) of the line through the points and

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