the equation for the line of best fit is y = 2x + 13. which statements are supported by this equation…

the equation for the line of best fit is y = 2x + 13. which statements are supported by this equation? select all that apply. a nail salon with 15 positive reviews will gain about 43 new clients in a month. on average, each additional positive review brings in an additional 2 new clients that month. a salon with no positive reviews should expect to gain no new clients. a salon that gained 53 new clients in a month had roughly 20 positive reviews.

the equation for the line of best fit is y = 2x + 13. which statements are supported by this equation? select all that apply. a nail salon with 15 positive reviews will gain about 43 new clients in a month. on average, each additional positive review brings in an additional 2 new clients that month. a salon with no positive reviews should expect to gain no new clients. a salon that gained 53 new clients in a month had roughly 20 positive reviews.

Answer

Explanation:

Step1: Analyze option A

Substitute $x = 15$ into $y=2x + 13$. Then $y=2\times15+13=30 + 13=43$. So option A is correct.

Step2: Analyze option B

In the linear - equation $y = 2x+13$, the slope is 2. The slope represents the change in $y$ (number of new clients) for a unit change in $x$ (number of positive reviews). So each additional positive review brings in 2 new clients on average, and option B is correct.

Step3: Analyze option C

Substitute $x = 0$ into $y=2x + 13$. Then $y=2\times0+13 = 13$. So a salon with no positive reviews should expect to gain 13 new clients, not 0. Option C is incorrect.

Step4: Analyze option D

Set $y = 53$ in the equation $y=2x + 13$. Then $53=2x+13$. Subtract 13 from both sides: $53 - 13=2x$, so $40 = 2x$. Divide both sides by 2: $x = 20$. Option D is correct.

Answer:

A. A nail salon with 15 positive reviews will gain about 43 new clients in a month. B. On average, each additional positive review brings in an additional 2 new clients that month. D. A salon that gained 53 new clients in a month had roughly 20 positive reviews.