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

Answers: 2

Show answers

Answers

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

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5

Answer from: Quest

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9