Lucy is saving money each week to save up for a new laptop. after 4 months she has $180. find the amount she has after 6 months if the equation that is represented by the scenario is y=20x+100 what does the 100 represent in the equation

$220 and 100 is y-intercept

Step-by-step explanation:

To start off the problem, what we have here is the a linear equation. A linear equation has symnols that represent itself. The equation is y= mx+b

y= outcome

m= slope (it can be negative, positive, a fraction or even a decimal!!!)

b= y-intercept or the value of "y" when "x" is zero

x= "x" value  (in this case it would be the amount of months!)

In this scenario it is showing the increase or decrease of what Lucy had earned. We know she earned money so, in this equation we see positive number.

Answering the question, we see the equation and we know the format of it and what it represent.

So in other words, what does the 100 represent? Well it represent the y-intercept if we graph this. Or we could say the 100 represent the amount of dollars Lucy had before saving up money for her laptop. We can also include from the linear equation is that Lucy is earning 20 dollars each month!

Besides that, the real question is how much does Lucy have after 6 months!? We can find the answer through many ways. We can answer by looking at a graph, solving it algebraically or even by a table!

Let try to solve it algebraically.

Step 1: Set up the equation that we are given

y= 20x+100

Step 2: Let replace "x" with the amount of months Lucy needs to know.

y= 20x+100

y= 20 (6) + 100

Step 3: Solve the equation. How?

y= 20 (6) + 100

y= 120 +100

y= 220

The answer is 220! So after 6 months, Lucy will have 220 dollars saved up for her new laptop!!

I hope you understand the problem and that I made it clear. If you have any questions or comment, PLEASE don't be afriad to ask! I would love to explain or even help out even further. I have attached a picture of solving the problem by algebraically and by a table! Again, hope I helped and have a great day!!!  

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation: