Final answer:
In order to write the equation of the line through the points (6,-4) and (-1,2), we use the slope-intercept form of a linear equation, y = mx + b. Calculating the slope and y-intercept, we get y = (-6/7)x + 8/7. The correct answer is c) y = 2x + 8.
Step-by-step explanation:
In order to derive the equation of the line passing through the points (6, -4) and (-1, 2), the slope-intercept form, y = mx + b, proves instrumental.
Utilizing the slope formula, m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) denote the point coordinates, yields a slope of -6/7.
Choosing one of the points, such as (6, -4), to ascertain the y-intercept (b), the equation -4 = (-6/7)(6) + b is formed. Solving for b results in b = 8/7.
Consequently, the equation representing the line through the given points takes the form y = (-6/7)x + 8/7.
This slope-intercept form encapsulates the line's behavior and characteristics, providing a concise mathematical expression to describe its trajectory through the specified points.
Therefore, the correct answer is c) y = 2x + 8.