Question

Javier begins to save for a new bicycle that costs $415. He already has $140 and plans to save $25 per week. Let w represent the number of weeks he has been saving and s(w) represent the total amount in dollars that he has saved. How long does he have to save to buy the bicycle?
a. Give the slope and the y-intercept of the function.

b. Write a linear function using the given information.

c. Describe how to use the function to answer the question, and then answer the question.​

Answer 1

Answer:

It will take 11 weeks of saving to buy the bicycle

Step-by-step explanation:

The Total amount he has saved for the bicycle can be expressed as;

Total amount saved=Initial amount he has+(savings per week×number of weeks)

where;

Initial amount he has=$140

Savings per week=$25

Number of weeks=w

Total amount saved=s(w)

replacing;

s(w)=140+(25×w)

The equation to get the total amount he has saved is;

s(w)=25 w+140....equation 1

Equation 1 above is a linear equation which can be written in the form;

y=mx+c

where;

y=s(w)

m=slope=25

x=the variable=w

c=y-intercept:the value of s(w), when w=o

s(w)=(25×0)+140=140

a). slope=25, y-intercept=140

b). Linear function is one of the form y=mx+c as explained above;

In our case, the linear function will be:

s(w)=25 w+140

c). Now that we have the function s(w)=25 w+140

In order to save to buy the bicycle;

we equate

s(w)=415 and solve for w;

415=25 w+140

25 w=(415-140)

25 w=275

w=275/25

w=11

It will take 11 weeks of saving to buy the bicycle