A line has slope of `1/6` and intersects the x-axis at `(-24,0)`. At which point does this line intersect the y-axis?

Answer

To find the point where the line intersects the y-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the slope and point of intersection**:
We are given that the slope (m) of the line is \( \frac{1}{6} \) and it intersects the x-axis at the point (-24, 0).

2. **Use the point-slope form of the line equation**:
The equation of a line in slope-intercept form is given by:
\[ y = mx + c \]
where \( m \) is the slope and \( c \) is the y-intercept.

3. **Substitute the known values into the equation**:
We know the slope \( m = \frac{1}{6} \). The point (-24, 0) gives us the coordinates where the line intersects the x-axis, which means when \( x = -24 \), \( y = 0 \). We substitute these values into the equation:
\[ 0 = \frac{1}{6} \times (-24) + c \]

4. **Solve for the y-intercept (c)**:
Simplifying the equation:
\[ 0 = -4 + c \]
Adding 4 to both sides gives:
\[ c = 4 \]

5. **Write the final equation of the line**:
Now that we have the value of \( c \), we can write the equation of the line:
\[ y = \frac{1}{6}x + 4 \]

6. **Find the intersection with the y-axis**:
The y-axis is where \( x = 0 \). We substitute \( x = 0 \) into the line equation:
\[ y = \frac{1}{6} \times 0 + 4 \]
This simplifies to:
\[ y = 4 \]

7. **State the coordinates of the intersection**:
Therefore, the coordinates where the line intersects the y-axis are:
\[ (0, 4) \]

### Final Answer:
The line intersects the y-axis at the point \( (0, 4) \).