Final answer:
To write the equation of a line passing through two points, find the slope using the formula (y2 - y1) / (x2 - x1). Then, substitute the slope and one of the points into the slope-intercept form y = mx + b to find the y-intercept. Finally, write the equation with the slope and y-intercept.
Step-by-step explanation:
To write the equation of the line that passes through the points (8, -4) and (-2, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b. First, we need to find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates of the two points, we get m = (5 - (-4)) / (-2 - 8) = 9 / -10. Now we can substitute one of the points and the slope into the equation to find the y-intercept (b). Using the point (8, -4), we get -4 = (9 / -10)(8) + b, which simplifies to b = -4 + 72 / 10 = 32 / 10 = 16 / 5. Now we can write the equation of the line as y = (9 / -10)x + 16 / 5.