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Conrad read a 180-page book cover to cover in a single session, at a constant rate. It took him 6 hours.
Let
y represent the number of pages left to read after
t hours.
Which of the following information about the graph of the relationship is given?
Choose 1 answer:
(A) Slope and
x-intercept
(B) Slope and
y-intercept
(C) Slope and a point that is not an intercept
(D)
x-intercept and
y intercept
(E)
y-intercept and a point that is not an intercept
(F) Two points that are not intercepts

Conrad read a $180$ -page book cover to cover in a single session, at a constant rate. It took him $6$ hours. $\newline$ Let $\newline$ $y$ represent the number of pages left to read after $\newline$ $t$ hours. $\newline$ Which of the following information about the graph of the relationship is given? $\newline$ Choose $1$ answer: $\newline$ (A) Slope and $\newline$ $x$ -intercept $\newline$ (B) Slope and $\newline$ $y$ -intercept $\newline$ (C) Slope and a point that is not an intercept $\newline$ (D) $\newline$ $x$ -intercept and $\newline$ $y$ intercept $\newline$ (E) $\newline$ $y$ -intercept and a point that is not an intercept $\newline$ (F) Two points that are not intercepts

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Interpret the slope and y-intercept of a linear function

Full solution

Q. Conrad read a

180

-page book cover to cover in a single session, at a constant rate. It took him

6

hours.

\newline

Let

\newline

y

represent the number of pages left to read after

\newline

t

hours.

\newline

Which of the following information about the graph of the relationship is given?

\newline

Choose

1

answer:

\newline

(A) Slope and

\newline

x

-intercept

\newline

(B) Slope and

\newline

y

-intercept

\newline

(C) Slope and a point that is not an intercept

\newline

(D)

\newline

x

-intercept and

\newline

y

intercept

\newline

(E)

\newline

y

-intercept and a point that is not an intercept

\newline

(F) Two points that are not intercepts

Determine reading rate: Determine the rate at which Conrad reads. $\newline$ Conrad read a $180$ -page book in $6$ hours, so his reading rate is the number of pages divided by the number of hours. $\newline$ Rate = $\frac{\text{Total pages}}{\text{Total time}}$ $\newline$ Rate = $\frac{180 \text{ pages}}{6 \text{ hours}}$ $\newline$ Rate = $30$ pages per hour
Write equation for pages left: Write the equation for the number of pages left to read after $t$ hours. $\newline$ Since Conrad reads at a constant rate, the number of pages he has left to read decreases linearly over time. The equation for the number of pages left, $y$ , after $t$ hours is: $\newline$ $y = \text{Total pages} - (\text{Rate} \times t)$ $\newline$ $y =$ $180$ - ( $30$ \times t)
Identify y-intercept: Identify the y-intercept of the graph. $\newline$ The y-intercept occurs when $t = 0$ , which is the starting point before Conrad begins reading. Plugging $t = 0$ into the equation gives us the y-intercept. $\newline$ $y = 180 - (30 \times 0)$ $\newline$ $y = 180$ $\newline$ The y-intercept is the point $(0, 180)$ , which represents the total number of pages Conrad has to read before he starts reading.
Identify slope: Identify the slope of the graph. $\newline$ The slope of the graph is the rate at which the number of pages left to read is changing with respect to time. In the equation $y = 180 - (30 \times t)$ , the coefficient of $t$ is $-30$ , which is the slope. $\newline$ Slope = $-30$ pages per hour
Determine x-intercept: Determine if there is an x-intercept and what it represents. $\newline$ The x-intercept occurs when $y = 0$ , which means there are no pages left to read. To find the x-intercept, set $y$ to $0$ and solve for $t$ . $\newline$ $0 = 180 - (30 \times t)$ $\newline$ $30 \times t = 180$ $\newline$ $t = \frac{180}{30}$ $\newline$ $t = 6$ $\newline$ The x-intercept is the point $(6, 0)$ , which represents the time it took Conrad to finish reading the book.
Choose correct answer: Choose the correct answer based on the information given. $\newline$ We have identified both the slope of the graph ( $-30$ pages per hour) and the y-intercept $(0, 180)$ . Therefore, the correct answer is: $\newline$ (B) Slope and y-intercept

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