Question 483·Easy·Algebra

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y = 15x + 30

Sofia is reading a novel. The equation above models the total number of pages $y$ she has read after $x$ days. Which of the following is the best interpretation of 30 in this context?

In a linear reading model, the y-intercept is the number of pages at day $0$ . To interpret the constant in the equation, set the day count to $0$ and read the result in pages. Keep the starting amount separate from the number multiplying the days: that coefficient gives the pages added each day.

Hints

Hint 1
The y-intercept is the output when the input is $0$ . Since $x$ counts days, day $0$ is when Sofia starts tracking. What does the equation give for $y$ at that point?
Hint 2
In $y=mx+b$ , $b$ is the starting amount, while $m$ is the amount added for each day. Which part of the given equation remains when $x=0$ ?

Step-by-step

Find the pages at day zero
Step 1
Find the starting page count
No Desmos needed. The constant’s meaning is visible by setting the day count to zero. The y-intercept is the output when $x=0$ . Since $x$ counts days, day $0$ is when Sofia starts tracking. Set $x=0$ in the equation:
$\begin{aligned} y&=15(0)+30\\[1.4em] y&=0+30\\[1.4em] y&=30 \end{aligned}$
Step 2
Interpret the pages at day zero
Because $y$ is the total number of pages read, $y=30$ at day $0$ means Sofia had already read $30$ pages before she started tracking. The constant is the starting number of pages; the number multiplying $x$ is the pages added each day. Here, $15$ is the daily rate, not $30$ . Choice C.

Question 483·Easy·Algebra

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