Math  /  Algebra

QuestionWarren just found his old journal in a drawer and has decided to start making 1 journal entry every day. There were already 8 entries in his journal.
Write an equation that shows how the total number of journal entries, yy, depends on the number of elapsed days, xx. y=y= \square Submition

Studdy Solution

STEP 1

What is this asking? How many total journal entries will Warren have after a certain number of days, if he starts with 8 entries and adds 1 new entry each day? Watch out! Don't forget about those **8 initial entries**!
It's easy to accidentally start counting from zero.

STEP 2

1. Define the function
2. Check the initial value

STEP 3

Alright, let's **define our function**!
We're going to use yy to represent the **total number of journal entries** and xx to represent the **number of days** that have passed.
Since Warren writes one entry per day, the number of *new* entries after xx days is simply 1x1 \cdot x, or just xx.

STEP 4

But hold on!
He *already* had **8 entries** in his journal.
So, to get the *total* number of entries (yy), we need to **add those initial 8 entries** to the *new* entries he makes.
This gives us the equation: y=x+8 y = x + 8 See? Super straightforward!

STEP 5

Let's do a quick sanity check!
At the very beginning, *before* any days have passed, xx is **zero**.
Plugging that into our equation: y=0+8 y = 0 + 8 y=8 y = 8 Perfect! This confirms that we start with **8 entries**, which is exactly what the problem told us.
Great job!

STEP 6

y=x+8 y = x + 8

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