Question

ter researching beach houses for an upco Each beach house charges a non- HOUSel:"SHORE THIN9 02 0 Total Cost ($) 100 1 3 Number of Nights

Answer 1

The beach house with the highest rate per night is House 2.

They charge $249 per night

Step-by-step explanation:

Given that the graph represent the rate at which House 1 charges;

We need to derive the equation for house 1.

Recall that the slope-intercept equation of a straight line can be represented by;

`y=mx+b`

where;

m = slope

b = y-intercept

Fro the given graph the y-intercept is at y=200, so;

`b=200`

we can also calculate the slope m using the formula;

`m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1)`

Substituting the coordinates on the graph;

`(0,200)\text{ and (4,1000)}`

we have;

`\begin{gathered} m=(1000-200)/(4-0) \\ m=(800)/(4) \\ m=200 \end{gathered}`

Therefore, we can write the equation for House 1 as;

`y=200x+200`

So, the equation for each house is;

`\begin{gathered} \text{House 1;} \\ y=200x+200 \\ \text{House 2;} \\ y=249x+100 \\ \text{House 3;} \\ y=230x+115 \end{gathered}`

where y is the total cost, x is the number of nights.

From the three equations, the beach house with the highest rate is House 2.

They charge $249 per night