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

Answer:

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 $=215$.

Step-by-step 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 $m=\frac{y_1-y}{x_1-x}$,plugging the values of the points.

$m=\frac{113.75-20}{25-0}=3.75$

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 $=215$.