Final answer:
The equation of the line through (4,-8) and (8,5) is y = 3.25x - 21, found by calculating the slope and applying the point-slope form.
Step-by-step explanation:
To complete the equation of the line through the points (4,-8) and (8,5), we need to find the slope (m) and the y-intercept (b) of the line. The slope can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.
The slope calculation: m = (5 - (-8)) / (8 - 4) = 13 / 4 = 3.25. With the slope and one point, we can use the point-slope form to find the equation. Let's use the point (4, -8): y - (-8) = 3.25(x - 4). Simplify this to get the slope-intercept form: y = 3.25x - 21.
This is the equation of the line passing through the points (4,-8) and (8,5).