Answer
$y_1 + y_3 = 2y_2$
Work Step by Step
For three points to lie on a straight line, they must satisfy the condition that the slope between any two points is the same.
Let's denote the points as \( (0, y_1) \), \( (1, y_2) \), and \( (2, y_3) \).
The slope between the first two points is:
\[ \frac{y_2 - y_1}{1 - 0} = y_2 - y_1 \]
The slope between the second and third points is:
\[ \frac{y_3 - y_2}{2 - 1} = y_3 - y_2 \]
For these three points to lie on a straight line, these slopes must be equal:
\[ y_2 - y_1 = y_3 - y_2 \]
This can be rearranged to:
\[ y_1 + y_3 = 2y_2 \]
So, the condition for the points \( (0, y_1) \), \( (1, y_2) \), and \( (2, y_3) \) to lie on a straight line is:
\[ y_1 + y_3 = 2y_2 \]
