Question

A line has a slope of 3 and passes through the point (0,9).
Complete the statement.
An equation of the line is
y = 3x + 9
-3x + y = -9
y - 9 = 3(x - 0)
y + 9 + = -3(x - 0)

Answer 1

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:

1. \( y = 3x + 9 \) - This is a correct equation of the line.
2. \( -3x + y = -9 \) - This can be rearranged to \( y = 3x - 9 \) which is incorrect.
3. \( y - 9 = 3(x - 0) \) - This correctly represents the point-slope form we started with.
4. \( y + 9 = -3(x - 0) \) - 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 \( y - 9 = 3(x - 0) \).