Respuesta :
Answer:
The beach house with the highest rate per night is House 2.
They charge $249 per night
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;
[tex]y=mx+b[/tex]where;
m = slope
b = y-intercept
Fro the given graph the y-intercept is at y=200, so;
[tex]b=200[/tex]we can also calculate the slope m using the formula;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the coordinates on the graph;
[tex](0,200)\text{ and (4,1000)}[/tex]we have;
[tex]\begin{gathered} m=\frac{1000-200}{4-0} \\ m=\frac{800}{4} \\ m=200 \end{gathered}[/tex]Therefore, we can write the equation for House 1 as;
[tex]y=200x+200[/tex]So, the equation for each house is;
[tex]\begin{gathered} \text{House 1;} \\ y=200x+200 \\ \text{House 2;} \\ y=249x+100 \\ \text{House 3;} \\ y=230x+115 \end{gathered}[/tex]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
