Answer:
460 = 250 + 35x
Explanation:
First, let's review some given knowledge. We know how much money he currently has, $250, and how much he plans to save per week, $35. We can represent this as a linear function in the form y = mx + b. The rate of change, aka the slope, is represented by m and the initial amount, aka the y-intercept, is b.
So what do m and b equal? We already have that knowledge! Because b represents the starting amount, we need to find the starting value of the savings account. That amount is $250, and so b = 250.
As for m, that, once more, is the rate of change. Here, that's how much money is added to the savings account in a frame of time. In this case, y represents how much money is in the savings account and x is how many weeks the student has been saving money for. In other words, the amount of money in the savings account is dependent on how many weeks the student has been saving money for.
This is for two reasons: first, in a linear equation of the form y = mx + b, x is the independent variable and y is the dependent variable. The function represents the change in x; this is why y could also be written as f(x),"the function of x" — y is a function of x. Second, it's very rare to find a situation where time is the dependent variable; you can go forward in time, but you (presumably!) can't go backward, unless you happen to have a DeLorean or a TARDIS.
Why is this important? Slope is rise over run; this could also be described as the change in y over the change in x, or
. Here, the slope is the change in the amount of money in the savings account over the number of weeks the student has been saving money. That's also the rate of change.
So, how much money is the student saving per week? The problem tells us that amount: he's saving $35 per week.
Now that we have our values, we can write our function. It is y = 35x + 250, where y is the amount of money in the savings account, x is the number of weeks the student has been saving money, 35 is the amount of money saved per week, and 250 is the starting amount of money in the account.
Next, we need to solve for a specific value of x. Here, y is given to us; it's 460, because the student wants to have $460 in his savings account. By substituting 460 for y, we turn our function into an equation. Then, we can solve for x, the number of weeks the student needs to reach his goal of having $460 in his savings account when he started with $250 and is saving $35 per week.
This, once again, makes our function, y = 35x + 250, into 460 = 35x + 250. Now, if we wanted to, we could solve for x by reversing the operations done. If this were a function, it would mean we were finding the inverse. But since this is an equation, we'd just be solving for x, the number of weeks the student will save money for until he reaches his goal.
Phew! This is a long explanation, I know. But my goal here is to help you understand the concept so you don't need to ask questions like this in the future. Hopefully, this answer helps you to reach that level.
It's about 9:00 AM where I am as I finish writing my answer, so good morning and have an awesome day! Keep learning, keep growing, and never stop going! You've got this!