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

Answer:

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

Step-by-step 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.

$m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

if we use points of option second then :

$\frac{12-7}{2-1} =m$

$5 = m$

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