Question

1. here is a graph that represents the quantities in this situation.

a. choose any point on the line.
state its coordinates, and explain
what it tells us.
b. choose any point that is not on
the line, state its coordinates, and
explain what it tells us.
lets discuss our work.

• what does the point \\((10,3)\\) mean in

this situation?

• is that a possible combination of

pounds of figs and almonds? why or
why not?

• from the graph, it looks like \\((7,3.5)\\) might be a solution, but it is hard to know for sure.

is there a way to verify?

1. a student has a savings account with \\(\\$ 475\\) in it. she deposits \\(\\$ 125\\) of her paycheck

into the account every week. her goal is to save \\(\\$ 7,000\\) for college.
a) how much will be in the account after 3 weeks?
b) how long will it take before she has \\(\\$ 1,350\\)?
c) write an equation that represents the relationship between the dollar amount in
er account and the number of weeks of saving.

Explanation:

Step1: Determine the initial amount and weekly deposit

The initial amount \(A_0 = 475\) dollars and the weekly deposit \(d=125\) dollars.

Step2: Solve part a)

The formula for the amount \(A\) after \(n\) weeks is \(A = A_0+dn\). For \(n = 3\), we substitute into the formula:
\(A=475 + 125\times3\)
\(A=475+375\)
\(A = 850\)

Step3: Solve part b)

We use the formula \(A = 475+125n\) and set \(A = 1350\). Then:
\(1350=475 + 125n\)
Subtract \(475\) from both sides: \(1350 - 475=125n\)
\(875 = 125n\)
Divide both sides by \(125\): \(n=\frac{875}{125}=7\)

Step4: Solve part c)

Let \(n\) be the number of weeks and \(A\) be the amount in the account. Using the slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept), here \(A\) is like \(y\), \(n\) is like \(x\), \(m = 125\) (weekly deposit) and \(b = 475\) (initial amount). So the equation is \(A=125n + 475\)

Answer:

a) \(\$850\)
b) \(7\) weeks
c) \(A = 125n+475\)