a. The inequality describing John's goal can be written as:
7x + 9y ≥ 693
The reason why we use the greater than or equal to sign (≥) is because John needs to earn at least $693, so the sum of his earnings from the job and mowing lawns should be greater than or equal to 693.
b. To graph the inequality, you can follow these steps:
1. Choose a scale for the x-axis and y-axis. Determine the maximum values for x and y based on the given information. For example, if you assume John can work a maximum of 100 hours at his job and mow lawns for a maximum of 100 hours, you can set the x-axis and y-axis from 0 to 100.
2. Plot the points on the graph. To get points, you can choose any combination of x and y values that satisfy the inequality. For example, you can choose (0, 77) which means John works 0 hours at his job and mows lawns for 77 hours. Other valid combination of x and y values could be (3, 68), (9, 63), (15, 56), etc.
3. Draw a line through the points. Since the inequality is greater than or equal to, the line should be solid to indicate that points on and above the line are included.
4. Shade the region above the line. This represents the solutions to the inequality because any point within or above the shaded region will satisfy the equation 7x + 9y ≥ 693.
Remember to label the x-axis, y-axis, and any important points on the graph.