Question

Ella runs a cat rescue center. She started with 2 cats, and her center has an increase of 5 cats per year. Which of the graphs below represents the number of cats per year at Ella's center?

graph of line going through 2, 5 and 5, 8
graph of line going through 1, 7 and 2, 12
graph of line going through 1, 1 and 3, 3
graph of line going through 1, 3 and 2, 8

Answer 1

Graph of line going through 1,7 and 2,12

Answer 2

B. Graph of line going through 1, 7 and 2, 12

Explanation:

Given : Ella started with 2 cats

Her center has an increase of 5 cats per year.

Solution : let x denotes the no. of years

So, every year increase of no. of cats is 5x .

And initially she had two cats .

So, every year no. hats she have (y) : 2+5x

Thus , y = 5x+2 is the required equation

comparing this equation with general form of equation of line i.e. y = mx +c

⇒ m = 5 (Slope of line )

in each option we are given two points

So, this m need to be calculated by formula of slope of two point line equation i.e.

`m=(y_(2) -y_(1) )/(x_(2) -x_(1) )`

if we use points of option second then :

`(12-7)/(2-1) =m`

`5 = m`

So, we are getting the same value of m which we got after compairing the equations .

hence, graph of line going through 1, 7 and 2, 12 is the correct one