Question

a caterer charges $120 fo cater 15 people and $200 for 25 people. Write an equation in slope-intercept form to model thus situation.

Answer 1

Step-by-step explanation:Write as two points in terms of: (number of people, cost in $)

�

(15,120) and (25,200)

�

Find the equation of the line using:

�

m = (y2 – y1) / (x2 – x1) and y = mx + b

�

Equation:

�

Y = 8x

�

plug in x = 40

�

y = 8(40) = 320

�

A party of 40 people will cost $320.00.

�

Slope:

�

m = 8 $/person

�

For every person that attends the party, the caterer’s bill increases by $120.00.

�

y-intercept: 0

�

(0,0)

�

This tells us that if no one attends the party, the caterer’s bill will be $0.00. So the

�

caterer has no base cost they charge to caterer a party.

�

Answer 2

We can model a linear relationship with the formula y = mx + b, where y is the cost, x is the number of people, m is the constant rate (increase in cost per person), and b represents the cost when no people are catered for (y-intercept).

To find the constant rate m, we need to know how much the cost increases per person catered for. In this case, the cost increases from $120 to $200 when the number of people goes from 15 to 25.

The increase in cost is $200 - $120 = $80
The increase in people is 25 people - 15 people = 10 people

The cost per person (slope, m) is thus found by dividing the increase in cost by the increase in people catered for, which gives m = $80 / 10 = $8.

To find the y-intercept (b), we subtract from the cost for 15 people the product of the slope and the number of people. That means, b = $120 - $8 * 15 = $0.

So the equation in slope-intercept form is y = 8x + 0 or simplifying, y = 8x.

This reflects the situation: the cost (y) is $8 times the number of people (x).