Question

Describing How to Create a Graph
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

Step-by-step:

1. Set up the axes. Label the horizontal axis x = hours and the vertical axis y = total cost ($). Choose a scale so the y-values fit easily (for example, x: 1 tick = 1 hour; y: 1 tick = $4 or $5; make sure you can show at least up to $28 or $40).

2. Plot the y-intercept. The line is y = 8x + 12, so when x = 0, y = 12. Plot the point (0, 12). This shows the instructor charges a $12 base fee even for 0 hours.

3. Use the slope to find a second point. The slope is 8, meaning the cost increases $8 for each extra hour (rise/run = 8/1). From (0,12) go right 1 and up 8 to plot (1,20). You can also use x = 2 → y = 28 to plot (2,28).

4. Draw the line. Use a ruler to draw a straight line through the plotted points, and extend it in both directions. Add arrows on the ends to show it continues. Label the line with its equation y = 8x + 12.

5. Optional notes: Because x is hours, realistically x ≥ 0, so only the portion of the line at and to the right of x = 0 represents valid costs. The range then is y ≥ 12 (costs of at least $12).