The constant term $30$ is the $y$-intercept. What does the equation tell you about $y$ when $x=0$?

In this situation, $x$ measures days. What moment in time does $x=0$ represent, and what would $y$ mean at that moment?

In Desmos, type y = 15x + 30 to graph the line.

On the graph, look at the point where the line crosses the $y$-axis (where $x=0$). Note the $y$-value at this point (it will be $30$) and think about what quantity $y$ represents at $x=0$ in the context of Sofia’s reading.

Notice that the equation $y = 15x + 30$ is in slope-intercept form:

where $m$ is the slope (rate of change) and $b$ is the $y$-intercept (starting value when $x=0$). In this equation, $m=15$ and $b=30$.

The problem says the equation models the total number of pages $y$ Sofia has read after $x$ days.

• $x$ = number of days
• $y$ = total pages read after $x$ days

So $m=15$ is the change in pages for each additional day (pages per day), and $b=30$ is the value of $y$ when $x=0$.

To understand $b=30$, plug in $x=0$:

So when $x=0$ (at the very start of the tracking period, before any days have passed), the model says Sofia has already read $30$ pages.

We found that $30$ is the total pages Sofia has read when $x=0$, before any days in the tracking period have gone by. That means $30$ represents how many pages she had already read before she started tracking her reading.

So the correct interpretation is: The number of pages Sofia had already read before she started tracking her reading.