Algebra-1

Question Analysis
This question assesses the ability to find the standard form of a linear equation given two points on the line. It requires calculating the slope, using point-slope form, and converting to standard form.

Key Concept Explanation
The standard form of a linear equation is $$Ax + By = C$$. Given two points, we can determine the slope, write the equation in point-slope form, and then convert it to standard form by rearranging terms.

Step-by-step Solution
1. Find the slope using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-8)}{-4 - 2} = \frac{3}{-6} = -frac{1}{2}$$
2. Use point-slope form with point $$(2, -8)$$: $$y - (-8) = -\frac{1}{2}(x - 2) \Rightarrow y + 8 = -\frac{1}{2}(x - 2)$$
3. Eliminate the fraction by multiplying both sides by 2: $$2(y + 8) = -1(x - 2)$...