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Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
Let
y represent the area (in square meters) left to paint after
x 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

Hiro painted his room. After $3$ hours of painting at a rate of $8$ square meters per hour, he had $28$ square meters left to paint. $\newline$ Let $\newline$ $y$ represent the area (in square meters) left to paint after $\newline$ $x$ 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. Hiro painted his room. After

3

hours of painting at a rate of

8

square meters per hour, he had

28

square meters left to paint.

\newline

Let

\newline

y

represent the area (in square meters) left to paint after

\newline

x

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

Calculate Initial Area: Determine the initial area left to paint before Hiro starts painting. $\newline$ Hiro has painted for $3$ hours at a rate of $8$ square meters per hour. To find the initial area, we add the area he has painted to the area left to paint. $\newline$ Calculation: $3$ hours $\times$ $8$ square meters/hour = $24$ square meters painted. The area left to paint after $3$ hours is $28$ square meters, so the initial area is $24$ square meters + $28$ square meters = $8$ $0$ square meters.
Write Equation Relationship: Write the equation that represents the relationship between the area left to paint ( extit{y}) and the hours spent painting ( extit{x}). $\newline$ Since Hiro paints at a constant rate, the slope ( extit{m}) of the line is the negative of the rate of painting because the area left to paint decreases as time increases. $\newline$ Calculation: Slope ( extit{m}) = $-8$ (since the area decreases by $8$ square meters per hour). $\newline$ The y-intercept ( extit{b}) is the initial area left to paint, which we found to be $52$ square meters. $\newline$ Equation: $y = -8x + 52$
Identify Given Information: Identify the given information based on the equation. $\newline$ We have the slope of the line, which is $-8$ , and the y-intercept, which is $52$ . The x-intercept is not given directly, but it could be calculated from the equation if needed. We also have a specific point on the line, which is $(3, 28)$ , representing the area left to paint after $3$ hours.
Match Information to Choices: Match the given information to the answer choices. $\newline$ We have the slope of the line and a specific point that is not an intercept $(3, 28)$ . This corresponds to answer choice (C) Slope and a point that is not an intercept.

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