The table shows the number of condo sales per month for a new building. Select all the equations that could represent the number of sales.

To determine which equations could represent the number of condo sales per month, we need to analyze each equation in the context of linear equations in the point-slope form, which is ( y – y_1 = m(x – x_1) ), where ( m ) is the slope and ( (x_1, y_1) ) is a point on the line.

1. A. ( y – 12 = -3(x – 1) )

This suggests a slope of -3, which indicates a decrease in sales over time. If sales were 12 at x = 1, it could represent a decline in sales. This equation is plausible.

2. B. ( y + 6 = -3(x + 3) )

This yields a slope of -3 as well and implies sales decrease with time starting from x = -3. While mathematically valid, it might not connect logically to sales starting from a non-negative month. This one is less likely.

3. C. ( y – 12 = 3(x – 1) )

This equation indicates a positive slope, meaning sales increase over time. If the sales were 12 at x = 1 and grew from there, it is a plausible representation.

4. D. ( y – 2 = -3(x – 9) )

Here, there is a negative slope of -3