Final answer:
The equation that represents the relationship between the number of weeks and the total amount of money Marcus will have saved is y = 5x + 42. After rearranging this equation into standard form, the correct answer is D. 5x + y = 42.
Step-by-step explanation:
To find the equation that represents the relationship between the number of weeks and the total amount of money Marcus will have saved, we can use the information given in the table. Marcus starts with $42 and saves an additional $5 each week. If we let x represent the number of weeks and y represent the total amount of money saved, the amount saved each week ($5) is multiplied by the number of weeks (x), and then we add the initial amount ($42) to find the total amount (y). So, the equation that describes this relationship is:
y = 5x + 42
Now, we need to rearrange this equation into standard form, which is Ax + By = C, where A, B, and C are integers and A is non-negative. After rearranging, we get:
5x - y = -42
Therefore, the correct answer from the options provided is C. −5x + y = 42, which after multiplying the entire equation by -1 to make 'x' coefficient positive, the standard form becomes D. 5x + y = 42.