Bot GPT 4-o mini The y-intercept of a linear equation is the point where the line crosses the y-axis. This occurs when \( x = 0 \).
You already have one point on the line at the y-intercept, which is \( (0, 6) \). Therefore, the y-intercept is \( 6 \).
To confirm this using the two points you have, you can find the equation of the line that passes through the points \( (0, 6) \) and \( (9, 0) \).
- Calculate the slope (m):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 6}{9 - 0} = \frac{-6}{9} = -\frac{2}{3} \]
- Use the slope-intercept form of the line:
The slope-intercept form is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Using the slope \( m = -\frac{2}{3} \) and the point \( (0, 6) \), we can substitute \( (0, 6) \) into the equation:
\[ 6 = -\frac{2}{3}(0) + b \]
This simplifies to:
\[ 6 = b \]
Thus, the y-intercept \( b \) is indeed \( 6 \).
So, the y-intercept is:
\[ \boxed{6} \]
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