Mathematics, 05.07.2019 13:00 jacelee17631

Acatering 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? guests total cost 30 $315 60 $555 that's the table^ $720 $795 $870 $945

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Answer from: mari200150

Second option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

Since the catering company uses a linear function to determine the total cost of parties, we can find the slope of the line with this formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

We can identify from the table that:

$y_2=315\\y_1=555\\\\x_2=30\\x_1=60$

Substittuting values, we get:

$m=\frac{315-555}{30-60}=8$

Now we can substitute the slope and one of the points on the table, into the equation y=mx+b and solve for "b":

$315=8(30)+b\\\\315-240=b\\\\b=75$

Then the linear function is:

y=8x+75

In order to calculate the cost (in dollars) to cater a dinner party with 90 guests, we must substitute x=90 into the equation and evaluate. Then, we get:

$y=8(90)+75\\\\y=795$

Answer from: mckennayoshz

The cost to cater a dinner party with 90 guests is $795

$\texttt{ }$

Further explanation

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

$\texttt{ }$

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

$\large {\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}}$

$\texttt{ }$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$\large {\boxed{y - y_1 = m ( x - x_1 )}}$

Let us tackle the problem.

$\texttt{ }$

This probem is about Linear Equation.

Let:

Line passes following coordinates:

( 30 , 315 ) → ( x₁ , y₁ )

( 60 , 555 ) → ( x₂ , y₂ )

We will use the formula as follows:

$\large {\boxed{m = \frac{555 - 315}{60 - 30}}}$

$m = \frac{240}{30}$

m = 8

$\texttt{ }$

y - y_1 = m ( x - x_1 )

y - 315 = 8 ( x - 30 )

y = 8x - 240 + 315

y = 8x + 75

$\texttt{ }$

The cost to cater a dinner party with 90 guests :

y = 8x + 75

y = 8(90) + 75

y = 720 + 75

$y = \boxed{795}$

$\texttt{ }$

Learn moreInfinite Number of Solutions : System of Equations : System of Linear equations : Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

Acatering company uses a linear function to determine the total cost of parties. the following table

Answer from: Quest

check above link.

graphically? well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

Answer from: Quest

your question is incomplete, write all the numbers in the sequence that it tells you.

step-by-step explanation:

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