Final answer:
The equation of the line passing through the points (-6, 4) and (3, 8) is y = (4/9)x + 20/9.
Step-by-step explanation:
To find the equation of the line passing through the points (-6, 4) and (3, 8), we need to determine the slope and the y-intercept of the line.
Step 1: Calculate the slope using the formula: m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, we get: m = (8 - 4) / (3 - (-6)) = 4 / 9
Step 2: Use one of the points and the slope to find the y-intercept, b, using the formula: y = mx + b
Plugging in the values, we get: 4 = (4/9)(-6) + b
Simplifying, we find: b = 20/9
Therefore, the equation of the line is: y = (4/9)x + 20/9