Respuesta :
Answer:
a) [tex] (x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105) [/tex]
And we want to find a function:
[tex] C (m) = b_1 m + b_0[/tex]
We can find the slope with this formula:
[tex] b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2[/tex]
And then we can use the point [tex] (x_1 = 225, y_1 = 80)[/tex] to find the intercept [tex] b_o[/tex] and we got:
[tex] 80 = 0.2*225 +b_0[/tex]
[tex] b_0 = 80-45 = 35[/tex]
So then the linear function is given by:
[tex] C(m) = 0.2 m + 35[/tex]
b) For this case we have that m = 475 so we can replace into the function to find the cost like this:
[tex] C(m =475) = 0.2*475 + 35 = 130[/tex]
And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:
[tex] 155 = 0.2m + 35[/tex]
[tex] 155-35= 120 = 0.2 m[/tex]
[tex] m= \frac{120}{0.2}= 600 mi[/tex]
Step-by-step explanation:
For this case we can define the following notation:
m= represent the miles travelled
C= represent the cost
Part a
For this case we have the following two points given:
[tex] (x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105) [/tex]
And we want to find a function:
[tex] C (m) = b_1 m + b_0[/tex]
We can find the slope with this formula:
[tex] b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2[/tex]
And then we can use the point [tex] (x_1 = 225, y_1 = 80)[/tex] to find the intercept [tex] b_o[/tex] and we got:
[tex] 80 = 0.2*225 +b_0[/tex]
[tex] b_0 = 80-45 = 35[/tex]
So then the linear function is given by:
[tex] C(m) = 0.2 m + 35[/tex]
Part b
For this case we have that m = 475 so we can replace into the function to find the cost like this:
[tex] C(m =475) = 0.2*475 + 35 = 130[/tex]
And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:
[tex] 155 = 0.2m + 35[/tex]
[tex] 155-35= 120 = 0.2 m[/tex]
[tex] m= \frac{120}{0.2}= 600 mi[/tex]
