Final answer:
The point-slope equation of the line passing through the points (8, -8) and (9, 8) is y = 16x - 136.
Step-by-step explanation:
The subject of this question is in Mathematics, specifically in the topic of Algebra. The question requires determining the point-slope equation of the line that passes through two given points (8, -8) and (9, 8). To find the equation of the line, we first need to calculate the slope which is given by the formula (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging the given points into this formula, we get (8 - (-8)) / (9 - 8) = 16. So, the slope of the line is 16.
We then use the point-slope form of the equation of a line, which is 'y - y1 = m(x - x1)', where m is the slope, and (x1, y1) any point on the line. Substituting our slope and one of our points into this formula, we get the equation of the line as 'y - (-8) = 16(x - 8)', or simplifying further, 'y + 8 = 16x - 128'. Finally, we rearrange to get 'y = 16x - 128 - 8', so the final equation of the line is y = 16x - 136.
Learn more about Point-Slope Equation