a catering company uses a linear function to determine the total cost of parties. the following table shows…

a catering company uses a linear function to determine the total cost of parties. the following table shows the costs for dinner parties with varied numbers of guests. what is the cost to cater a dinner party with 90 guests?\n| guests | total cost |\n| ---- | ---- |\n| 30 | $315 |\n| 60 | $555 |\n$720\n$795\n$870\n$945

a catering company uses a linear function to determine the total cost of parties. the following table shows the costs for dinner parties with varied numbers of guests. what is the cost to cater a dinner party with 90 guests?\n| guests | total cost |\n| ---- | ---- |\n| 30 | $315 |\n| 60 | $555 |\n$720\n$795\n$870\n$945

Answer

Explanation:

Step1: Find the slope of the linear - function

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the number of guests and $y$ be the total cost. Using the points $(x_1,y_1)=(30,315)$ and $(x_2,y_2)=(60,555)$, we have $m=\frac{555 - 315}{60 - 30}=\frac{240}{30}=8$.

Step2: Find the y - intercept of the linear function

Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Substitute $m = 8$, $x_1 = 30$, and $y_1 = 315$ into $y - y_1=m(x - x_1)$: $y-315=8(x - 30)$. Expand: $y-315=8x-240$. Then $y=8x + 75$.

Step3: Calculate the cost for 90 guests

Substitute $x = 90$ into the equation $y=8x + 75$. So $y=8\times90+75=720 + 75=795$.

Answer:

$795$