To determine which point is also on the line containing the points (0, 9) and (6, 6), we can use the concept of calculating the slope of the line. The formula for slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Given points (0, 9) and (6, 6), we can calculate the slope:
m = (6 - 9) / (6 - 0)
m = -3 / 6
m = -1/2
Now, we can test each of the given points to see which one lies on the line with the calculated slope:
1. Point F (2, 5):
m = (5 - 9) / (2 - 0) = -4 / 2 = -2 (not equal to -1/2)
Therefore, point F (2, 5) is not on the line.
2. Point G (4, 7):
m = (7 - 9) / (4 - 0) = -2 / 4 = -1/2
Since the calculated slope matches the slope of the line, point G (4, 7) is on the line.
3. Point H (-8, 5):
m = (5 - 9) / (-8 - 0) = -4 / -8 = 1/2 (not equal to -1/2)
Therefore, point H (-8, 5) is not on the line.
4. Point I (4, 4):
m = (4 - 9) / (4 - 0) = -5 / 4
This point's slope doesn't match the line's slope, so point I (4, 4) is not on the line.
In conclusion, the point (4, 7) represented by choice G is the point that also lies on the line passing through (0, 9) and (6, 6).
