Final answer:
The equation of the line in point-slope form that goes through the points (-5, 4) and (10, -2) is y - 4 = (-2/5)(x + 5), with a calculated slope of -2/5.
Step-by-step explanation:
The student is asking for the equation of the line in point-slope form that passes through the points (-5, 4) and (10, -2). To find the equation of this line, we first need to calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula, we have:
- m = (-2 - 4) / (10 - (-5))
- m = (-6) / (15)
- m = -2/5
Now that we have the slope, we can use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1). Using the point (-5, 4):
- y - 4 = (-2/5)(x - (-5))
- y - 4 = (-2/5)(x + 5)
Hence,
the equation of the line in point-slope form that goes through the points (-5, 4) and (10, -2) is y - 4 = (-2/5)(x + 5).