a landscaper makes a $2,000 profit in a week when he services 25 lawns. he makes a $600 profit in a week…

a landscaper makes a $2,000 profit in a week when he services 25 lawns. he makes a $600 profit in a week when he services 11 lawns. if his profit for the week is a linear function of the number of lawns serviced, how much profit would he receive in a week that he services 36 lawns?\n$2,600\n$2,880\n$3,100\n$3,600

a landscaper makes a $2,000 profit in a week when he services 25 lawns. he makes a $600 profit in a week when he services 11 lawns. if his profit for the week is a linear function of the number of lawns serviced, how much profit would he receive in a week that he services 36 lawns?\n$2,600\n$2,880\n$3,100\n$3,600

Answer

Explanation:

Step1: Find the slope of the linear - function

Let $x$ be the number of lawns serviced and $y$ be the profit. We have two points $(x_1,y_1)=(25,2000)$ and $(x_2,y_2)=(11,600)$. The slope $m$ of the line is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. $m=\frac{600 - 2000}{11 - 25}=\frac{- 1400}{-14}=100$

Step2: Find the y - intercept of the linear function

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(x_1,y_1)=(25,2000)$ and $m = 100$. $y-2000=100(x - 25)$ $y-2000=100x-2500$ $y=100x - 500$

Step3: Calculate the profit for 36 lawns

Substitute $x = 36$ into the equation $y=100x - 500$. $y=100\times36-500$ $y=3600 - 500=3100$

Answer:

$3100$ (corresponding to option C. $3100$)