Question

Write an equation for this graph in slope-intercept form

y = 3x + 5

y = 1/3 * x + 6

y = 6x + 1/3

y = 3x + 6

The slope intercept is (0,6)

Answer 1

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
1. You provided multiple equations:
- \( y = 3x + 5 \)
- \( y = \frac{1}{3}x + 6 \)
- \( y = 6x + \frac{1}{3} \)
- \( y = 3x + 6 \)

2. 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:

1. \( y = \frac{1}{3}x + 6 \) (slope of \( \frac{1}{3} \))
2. \( y = 3x + 6 \) (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.