To confirm and derive a slope-intercept equation based on the details given:
Slope-Intercept Form
The slope-intercept form of a linear equation is given by: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept.
Given Information
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You provided multiple equations:
- \( y = 3x + 5 \)
- \( y = \frac{1}{3}x + 6 \)
- \( y = 6x + \frac{1}{3} \)
- \( y = 3x + 6 \)
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You mentioned "The slope intercept is (0,6)", which indicates that the y-intercept \( b = 6 \).
Identifying the Relevant Equation
Since the y-intercept at \( (0,6) \) indicates \( b=6 \), we can narrow it down to the equations that include \( b = 6 \):
- \( y = \frac{1}{3}x + 6 \)
- \( y = 3x + 6 \)
Conclusion
To write an equation for the graph that uses the y-intercept given, we can use either of the two equations identified:
- \( y = \frac{1}{3}x + 6 \) (slope of \( \frac{1}{3} \))
- \( y = 3x + 6 \) (slope of \( 3 \))
Final Answer
Based on the requirement for the slope-intercept form with a y-intercept of 6, both \( y = \frac{1}{3}x + 6 \) and \( y = 3x + 6 \) are valid. Choose one based on the slope preference.