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

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$x_1=0,y_1=2$

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

$x_2=20 , y_2=7$

now, we can plug these values

$m=\frac{7-2}{20-0}$

$m=\frac{1}{4}$

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

$y=\frac{1}{4}x+2$..........Answer

(B)

we are given

number of engines =50

so, we can plug x=50 and find y

$y=\frac{1}{4}*50+2$

$y=14.5$

so, y=14.5 thousand dollars

y=14.5*1000=$14500

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