Question

The graph shows the total cost (y) of producing x motorbike engines.

Answer 1

B. 0.25x+2

C. $14,500

Answer 2

We are given

total cost is y thousand dollars

number of engines produced is x

We can select any two points

so, we can select those two points as

(0,2) and (20,7)

Let's assume

`(x_1,y_1)=(0,2)`

`(x_2,y_2)=(20,7)`

(A)

Since, we have to find equation of line y

so, we can use slope intercept form of line

that is

`y=mx+b`

where

m is slope

b is y-intercept

step-1:Finding slope (m)

we can use formula

`m=(y_2-y_1)/(x_2-x_1)`

`(x_1,y_1)=(0,2)`

`x_1=0,y_1=2`

`(x_2,y_2)=(20,7)`

`x_2=20 , y_2=7`

now, we can plug these values

`m=(7-2)/(20-0)`

`m=(1)/(4)`

step-2: Finding y-intercept (b)

we know that

y-intercept is value of y when x=0

we are given (0,2)

so,

`b=2`

step-3: Finding equation of line

we can find equation of line

`y=(1)/(4)x+2`..........Answer

(B)

we are given

number of engines =50

so, we can plug x=50 and find y

`y=(1)/(4)*50+2`

`y=14.5`

so, y=14.5 thousand dollars

y=14.5*1000=$14500

The total cost of producing 50 engines is $14500..........Answer