Question

In 2005, Kailee had $500 in her savings account. In 2015, she had

$1,250 in her savings account. Using a linear model, what does the y-
intercept represent if x is the number of years since the year 2000?
A. Kailee had $500 in her savings account in the year 2000.
B. Kailee had $125 in her savings account in the year 2000.
C. Kailee saved $75 each year.
D. Kailee saved $50 each year.

Answer 1

B. Kailee had $125 in her savings account in the year 2000.

Step-by-step explanation:Let

Let

x ----> the number of years since the year 2000

y ---> amount in her savings account

we know that

The year 2000 represent x=0

so

2005 represent x=5 years

2015 represent x=15 years

we have the ordered pairs

(5,500) and (15,1,250)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(1,250-500)/(15-5)`

`m=75`

Find the equation of the line in slope intercept form

`y=mx+b`

we have

`m=75`

point (5,500)

substitute and solve for b

`500=75(5)+b\\b=500-375\\b=\$125`

therefore

The y-intercept is $125 (amount of money in the saving accounts in the year 2000)