Final answer:
The equation of the line passing through the points (-8,-8) and (4,1) is y = (3 / 4)x - 2.
Step-by-step explanation:
The equation of the line passing through the points (-8,-8) and (4,1) can be found using the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we use the formula m = (y2 - y1) / (x2 - x1). Plugging in the values of the given points, we get m = (1 - (-8)) / (4 - (-8)) = 9 / 12 = 3 / 4.
Next, we can choose either point to find the y-intercept. Let's use (-8, -8). Plugging in the values of x, y, and m, we get -8 = (3 / 4)(-8) + b. Solving for b, we get b = -8 + 6 = -2.
Therefore, the equation of the line is y = (3 / 4)x - 2.