Final answer:
The equation for the line that passes through the points (6, -5) and (-8, 16) is y = 3x - 14.
Step-by-step explanation:
To find the equation of a line that passes through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m) using the formula: m = (y2 - y1)/(x2 - x1). Plugging in the values from the given points, we get: m = (16 - (-5))/(-8 - 6) = 21/14 = 3/2.
Next, we can choose one of the points to substitute into the equation and find the y-intercept (b). Let's use (6, -5): -5 = (3/2)(6) + b. Solving for b, we get b = -5 - 9 = -14.
Therefore, the equation for the line that passes through the points (6, -5) and (-8, 16) is y = (3/2)x - 14. Therefore, the correct answer is A. y = 3x - 14.