To find an equation of the line with a slope of 3 that passes through the point (0, 9), we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope. In this case, \( (x_1, y_1) = (0, 9) \) and \( m = 3 \).
Using the point-slope form:
\[ y - 9 = 3(x - 0) \]
This simplifies to:
\[ y - 9 = 3x \]
Which can be rewritten in slope-intercept form (y = mx + b) as:
\[ y = 3x + 9 \]
Now let's evaluate the other options given:
- \( y = 3x + 9 \) - This is a correct equation of the line.
- \( -3x + y = -9 \) - This can be rearranged to \( y = 3x - 9 \) which is incorrect.
- \( y - 9 = 3(x - 0) \) - This correctly represents the point-slope form we started with.
- \( y + 9 = -3(x - 0) \) - This simplifies to \( y = -3x - 9 \), which is also incorrect since the slope is 3, not -3.
Therefore, the correct equation of the line is:
An equation of the line is: \( y = 3x + 9 \) or \( y - 9 = 3(x - 0) \).