Question

the scatter plot below shows the number of pages scanned (y) in different number of hours (x) by a scanning machine: plot ordered pairs 0, 500 and 1, 1500 and 2, 2500 and 3, 3500 and 4, 4500 and 5, 5500 which function best represents the data shown in the scatter plot?

Answer 1

slope(m) = 1000

y = mx + b....(0,500)
500 = 1000(0) + b
500 = b

y = 1000x + 500
f(x) = 1000x + 500

Answer 2

`y=1000x + 500`

Explanation:

Ordered pairs : number of hours (x) , number of pages scanned (y)

(0,500)

(1,1500)

(2,2500)

(3,3500)

(4,4500)

(5,5500)

Now we will use two point slope form :

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

`(x_1,y_1)=(0,500)`

`(x_2,y_2)=(1,1500)`

Substituting the value in two pint slope form:

`y-500=(1500-500)/(1-0)(x-0)`

`y-500=1000x`

`y=1000x + 500`

Hence The function best represents the data shown in the scatter plot :

`y=1000x + 500`