Question

a small - town library has 9,904 books. the library plans to add 450 books each year. what is the slope - intercept form of the equation of the line that models this situation? the independent variable represents time in years, and the dependent variable represents the number of books in the library.
\\(\circ\\) \\(y = 450x+9,904\\)
\\(\circ\\) \\(y = 9,904x + 450\\)
\\(\circ\\) \\(y = 450x-9,904\\)
\\(\circ\\) \\(y = 9,904x-450\\)

question 5
1 point
cali decides to start a rock collection upon being given 5 pieces of quartz by her grandmother. her goal is to add a certain number of rocks to her collection each week. on day 11, she will have 49 rocks if she can keep up with her goal. what is the slope - intercept form of the equation of the line that models this situation? the independent variable represents time in days. the dependent variable represents the total number of rocks in her collection.
(fill each blank with an integer.)
\\(y = \square x+\square\\)

Explanation:

First Question

Step1: Recall slope-intercept form

Slope-intercept form is $y=mx+b$, where $m$ = slope (rate of change), $b$ = y-intercept (initial value).

Step2: Identify $m$ and $b$

Initial books $b=9904$, weekly addition $m=450$.

Step3: Substitute into formula

$y = 450x + 9904$

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Second Question

Step1: Recall slope-intercept form

Slope-intercept form is $y=mx+b$, where $m$ = slope, $b$ = initial value.

Step2: Identify initial value $b$

Initial rocks $b=5$.

Step3: Calculate slope $m$

Use point $(x_1,y_1)=(0,5)$ and $(x_2,y_2)=(11,49)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{49-5}{11-0}=\frac{44}{11}=4$

Step4: Substitute into formula

$y = 4x + 5$

Answer:

$y = 450x + 9,904$