Final answer:
To find points on a line with a slope of -1/5 that passes through (-8, 12), move horizontally by increments of 5 units and adjust the y-coordinate by a decrease of 1 unit each time. Following this pattern gives us the points (-3, 11), (2, 10), and (7, 9).
Step-by-step explanation:
To find three other points that a line with a slope of -1/5 passes through, starting from the point (-8, 12), we can use the slope to determine the vertical change (rise) for a given horizontal change (run). Because the slope is negative, as we move to the right along the x-axis (horizontal axis), we will move down on the y-axis (vertical axis).
Let's choose a run of +5 units (since the denominator of the slope is 5). This choice will simplify our calculations, as multiplying the slope by the run (+5) gives us a rise of -1 (since -1/5 × 5 = -1).
- Moving 5 units to the right from x = -8, we get x = -3. The y-coordinate decreases by 1, so y = 12 - 1 = 11. Thus, one new point is (-3, 11).
- Moving another 5 units to the right, we get x = 2, and again the y-coordinate decreases by 1, so y = 11 - 1 = 10. This gives us the point (2, 10).
- For the third point, moving 5 more units to the right, we reach x = 7, and y decreases by another 1, giving us y = 10 - 1 = 9. Hence, the third point is (7, 9).
Therefore, the three additional points on the line with a slope of -1/5 that passes through the point (-8, 12) are (-3, 11), (2, 10), and (7, 9).