Question

PLEASE HELP !!!!!!! Jordan got a new money bank for his birthday with $20 inside. He puts part of his weekly allowance in his bank each week and doesn’t take anything out. He puts the same amount in each week. After 25 weeks, he has $113.75 in his bank. The amount of money in Jordan’s bank can be represented by a linear function.

Question 1
Part A

What are the slope and y-intercept of this function?

The slope of the function is _
, and the y-intercept is _
.
Question 2
Part B
Use the drop-down menus to complete the statements.

The equation y =_____ x can represent the function described.

The initial value is .__

Jordan puts__ in his bank each week.

After 52 weeks, Jordan will have ___

Answer 1

Slope of the function is
`=3.75`,Y-intercept
`=20`.

The function is
`y=3.75(x)+20` with initial value
`=20`,Jordan puts
`\$3.75` each week andthe amount saved by Jordan after
`52` week
`=215\$`.

Explanation:

To understand the slope and y-intercept lets assign
`x` as number of weeks and
`y` as the money saved by Jordan.

Jordan is already having a sum of
`\$20` inside the money bank so in
`0` week the amount is
`\$20` can be written as
`(x,y) =(0,20)` in coordinate form.

SImilarly

We have
`(x,y) =(0,20)`and
`(x_1,y_1) =(25,113.75)`

Part A:

The function is
`y=m(x)+b`

From point-slope form,we have slope (m)

and
`m=(y_1-y)/(x_1-x)`,plugging the values of the points.

`m=(113.75-20)/(25-0)=3.75`

Y-intercept of this function is the constant term or the money of
`\$20` that is already inside the money bank.

We can also calculate y-intercept by arranging the function as
`b=y-m(x)` choosing any
`(x_1,y_1) = (25,113.75)` coordinate and here
`b` is the y-intercept.

The result will be same.

Part B:

The equation
`y=3.75(x)` can represent the function described.

And the initial value is the y-intercept
`=\$20`

Jordan puts
`3.75` in his bank each week.

After
`52` week the amount saved by Jordan ,here
`x=52`,as the x-variable is the number of weeks.

Plugging the value of
`x=52` in
`y=m(x)+b` where
`m=3.75` so the equation becomes
`y=3.75(x)+20`

`y=3.75(x)+20 =3.75(52)+20=\$215`

So basically the function is
`y=3.75(x)+20` and the amount saved by Jordan after
`52` week
`=215\$`.