The rule that all the points except one lie on the same line can be expressed algebraically using the equation of a line in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the rule, we need to calculate the slope (m) of the line that passes through the points A(2, 3), B(4, 6), C(-6, -9), and D(5, 9).
Let's calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
1. Slope between points A and B:
m_AB = (6 - 3) / (4 - 2) = 3 / 2
2. Slope between points B and C:
m_BC = (-9 - 6) / (-6 - 4) = -15 / -10 = 3/2
3. Slope between points C and D:
m_CD = (9 - (-9)) / (5 - (-6)) = 18 / 11
4. Slope between points D and A:
m_DA = (3 - 9) / (2 - 5) = -6 / -3 = 2
Since the slopes are not the same for all the pairs of points, they do not lie on the same line except for points A and B.
Therefore, the algebraic rule for the points that lie on the same line is y = (3/2)x + (0), and the point that does not follow this rule is point E(0, 0).
