Write an equation that shows how the total number of journal entries, y, depends on the number of elapsed days, x.
Understand the Problem
The question is asking for an equation that relates the total number of journal entries, y, to the number of days elapsed, x. Warren has 8 entries initially and adds 1 entry each day. To solve this, we will create a linear equation based on the initial entries and the rate of increase.
Answer
The equation for the total number of journal entries is $y = x + 8$.
Answer for screen readers
The equation that shows how the total number of journal entries, $y$, depends on the number of elapsed days, $x$, is given by:
$$ y = x + 8 $$
Steps to Solve
-
Identify the initial condition Warren starts with 8 journal entries. This represents the initial value in the equation, often called the y-intercept.
-
Determine the rate of increase Warren adds 1 journal entry each day. This constant addition represents the slope of the equation, which indicates how much the total entries increase with each passing day.
-
Write the linear equation The general form of a linear equation is given by:
$$ y = mx + b $$
where $m$ is the slope and $b$ is the y-intercept. For this problem, we have:
- $m = 1$ (the number of entries added each day)
- $b = 8$ (the initial number of entries)
Thus, substituting these values into the equation, we have:
$$ y = 1x + 8 $$
- Simplify the equation The equation can be simplified to:
$$ y = x + 8 $$
This shows how the total number of journal entries, $y$, depends on the number of elapsed days, $x$.
The equation that shows how the total number of journal entries, $y$, depends on the number of elapsed days, $x$, is given by:
$$ y = x + 8 $$
More Information
This equation represents a simple linear relationship where every day Warren adds one new entry to his journal. The total number of entries will consistently increase by one for each day that passes.
Tips
- Forgetting to include the initial value of entries (8) when formulating the equation.
- Confusing the slope with the initial value; the slope represents the daily addition, while the initial value is the starting point.
AI-generated content may contain errors. Please verify critical information
