Question

The equation y = 8x + 12, where x is the number of hours and y is the total cost, represents what the surf instructor charges for lessons. Use this information to describe how to draw the line on a graph.

Answer 1

To graph the equation \( y = 8x + 12 \), follow these steps:

1. **Identify the slope and y-intercept**:
The equation is in the slope-intercept form \( y = mx + b \), where:
- \( m \) (slope) is 8
- \( b \) (y-intercept) is 12

This means that the line crosses the y-axis at 12 and has a slope of 8, which means that for every increase of 1 hour (1 unit along the x-axis), the cost increases by 8 dollars (8 units along the y-axis).

2. **Plot the y-intercept**:
Begin by plotting the y-intercept, which is the point (0, 12). This is where the line crosses the y-axis.

3. **Use the slope to find additional points**:
The slope of 8 can also be represented as a fraction: \( \frac{8}{1} \). This means that from the y-intercept (0, 12), you can move up 8 units and to the right 1 unit to plot another point:
- Start at (0, 12)
- Move up 8 units to y = 20 (from 12 to 20)
- Move right 1 unit to x = 1
- This gives you the point (1, 20).

4. **Plot more points using the slope**:
Repeat this process to find more points. For example:
- From (1, 20), moving up 8 units and right 1 unit gives (2, 28).
- From (2, 28), moving up 8 units and right 1 unit gives (3, 36).

5. **Draw the line**:
Once you have at least two points plotted (more if you want greater accuracy), use a ruler to draw a straight line through these points, extending it in both directions. Make sure to draw arrows at both ends indicating that the line continues indefinitely.

6. **Label your graph**:
Label your axes as follows:
- The x-axis can be labeled "Hours (x)".
- The y-axis can be labeled "Total Cost (y)".
- You may also want to label the line with its equation \( y = 8x + 12 \).

By following these steps, you'll effectively represent the cost of surf lessons based on the number of hours in a clear and visually accurate graph.