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Gaia is driving her truck from Paris to Lyon. The function
D gives the total distance Gaia has driven (in kilometers) after
t hours.
What is the best interpretation for the following statement?
The slope of the line tangent to the graph of
D at
t=3 is equal to 90 .
Choose 1 answer:
(A) During the first 3 hours, Gaia drove 90 kilometers per hour.
B) At time 3, Gaia drove at a rate of 90 kilometers.
(C) 3 hours after leaving, Gaia was 90 kilometers away from Paris.
(D) 3 hours after leaving, Gaia drove at a rate of 90 kilometers per hour.

Gaia is driving her truck from Paris to Lyon. The function $D$ gives the total distance Gaia has driven (in kilometers) after $t$ hours. $\newline$ What is the best interpretation for the following statement? $\newline$ The slope of the line tangent to the graph of $D$ at $t=3$ is equal to $90$ . $\newline$ Choose $1$ answer: $\newline$ (A) During the first $3$ hours, Gaia drove $90$ kilometers per hour. $\newline$ (B) At time $3$ , Gaia drove at a rate of $90$ kilometers. $\newline$ (C) $3$ hours after leaving, Gaia was $90$ kilometers away from Paris. $\newline$ (D) $3$ hours after leaving, Gaia drove at a rate of $90$ kilometers per hour.

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Interpreting Linear Expressions

Full solution

Q. Gaia is driving her truck from Paris to Lyon. The function

D

gives the total distance Gaia has driven (in kilometers) after

t

hours.

\newline

What is the best interpretation for the following statement?

\newline

The slope of the line tangent to the graph of

D

at

t=3

is equal to

90

.

\newline

Choose

1

answer:

\newline

(A) During the first

3

hours, Gaia drove

90

kilometers per hour.

\newline

(B) At time

3

, Gaia drove at a rate of

90

kilometers.

\newline

(C)

3

hours after leaving, Gaia was

90

kilometers away from Paris.

\newline

(D)

3

hours after leaving, Gaia drove at a rate of

90

kilometers per hour.

Rate of Change Definition: The slope of a line tangent to a graph at a certain point represents the rate of change at that point.
Speed Calculation: Since $D$ represents total distance driven and $t$ represents time, the slope represents the speed at time $t$ .
Tangent Line Slope at $t=3$ : The statement says the slope of the line tangent to the graph of $D$ at $t=3$ is equal to $90$ . This means at $t=3$ , the speed is $90$ kilometers per hour.

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