Question

Graph the line with the equation y, equals, one sixth, x, plus, 4y=
6
1
​
x+4.

Answer 1

To graph the line represented by the equation \( y = \frac{1}{6}x + 4 \), we can follow these steps:

1. **Identify the slope and y-intercept**:
- Here, the equation is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- The slope (\( m \)) is \( \frac{1}{6} \), and the y-intercept (\( b \)) is \( 4 \). This means the line crosses the y-axis at 4.

2. **Plot the y-intercept**:
- Start by plotting the point \( (0, 4) \) on the graph. This is where your line will cross the y-axis.

3. **Use the slope to find another point**:
- The slope of \( \frac{1}{6} \) means that for every 6 units you move to the right (positive direction on the x-axis), you move up 1 unit (positive direction on the y-axis).
- From the point \( (0, 4) \), move 6 units to the right to \( (6, 4) \), and then 1 unit up to \( (6, 5) \). Plot this point.

4. **Draw the line**:
- Connect the two points \( (0, 4) \) and \( (6, 5) \) with a straight line, and extend it in both directions.

5. **Determine some additional points for accuracy (optional)**:
- You can calculate a few additional points by plugging in values for \( x \):
- For \( x = 6 \):
\[ y = \frac{1}{6}(6) + 4 = 1 + 4 = 5 \] → Point \( (6, 5) \)
- For \( x = 12 \):
\[ y = \frac{1}{6}(12) + 4 = 2 + 4 = 6 \] → Point \( (12, 6) \)
- For \( x = -6 \):
\[ y = \frac{1}{6}(-6) + 4 = -1 + 4 = 3 \] → Point \( (-6, 3) \)

6. **Final graph**:
- On a coordinate plane, plot the points you calculated and draw a line through them, ensuring it continues in both directions.

This is how you graph the line with the given equation. If you would like to visualize it, you can use graphing software or graph paper to accurately represent these points and the line.