Bot GPT 4-o mini The points (6, 0) and (9, 0) indicate that both of these points are on the x-axis, specifically where \( y = 0 \). The y-intercept of a graph is the point where the graph crosses the y-axis, which occurs when \( x = 0 \).
To find the y-intercept, we need to determine if the points (6, 0) and (9, 0) lie on a line, and if so, determine the equation of that line. The vertical position of the line (its y-value) will help us find the y-intercept.
Since both points have a y-value of 0, if we were to express the line passing through these points as a linear equation:
- Identify the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 0}{9 - 6} = \frac{0}{3} = 0 \]
This indicates that the line is horizontal.
- The equation of a horizontal line is given by \( y = b \), where \( b \) is the constant y-value. Given that the line passes through the points (6, 0) and (9, 0), we find:
\[ y = 0 \]
This means the line does not intersect the y-axis except at \( y = 0 \).
Thus, the y-intercept of the graph is:
\[ \boxed{0} \]
The line itself doesn't cross the y-axis at any point other than the origin (0, 0).
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