An electric vehicle is connected to a charging station. The energy stored in the vehicle's… — SAT

An electric vehicle is connected to a charging station. The energy stored in the vehicle's battery pack, $E$ , in kilowatt-hours (kWh), can be modeled by the equation $E = 0.75m + 24.0$ , where $m$ is the number of minutes the vehicle has been charging. Which of the following is the best interpretation of the number $0.75$ in this context?

A
The initial energy stored in the battery pack, in kilowatt-hours, before the vehicle began charging
B
The increase in the charging time, in minutes, for each additional kilowatt-hour of energy stored in the battery pack
The increase in the energy stored in the battery pack, in kilowatt-hours, for each additional minute the vehicle is chargedAnswer
D
The total energy stored in the battery pack, in kilowatt-hours, after the vehicle has been charging for $1$ minute

Answer

The increase in the energy stored in the battery pack, in kilowatt-hours, for each additional minute the vehicle is charged

The coefficient of

m

in the linear equation

E = 0.75m + 24.0

is the slope of the line. In context, the slope represents the rate of change of the dependent variable (stored energy,

E

) per unit increase of the independent variable (time,

m

). Thus,

0.75

represents an increase of

0.75

kilowatt-hours in stored energy for each additional minute of charging.

Step-by-Step Solution

Identify the form and components of the given equation.

The equation

E = 0.75m + 24.0

is in the slope-intercept form

y = mx + b

, where

m = 0.75

is the slope and

b = 24.0

is the y-intercept.

To relate the numerical values in the equation to their mathematical interpretations.

Interpret the meaning of the slope in context.

The slope,

0.75

, represents the unit rate of change of the dependent variable (energy

E

in kWh) per unit change of the independent variable (time

m

in minutes).

To explain what the coefficient of

m

means in real-world terms.

Combine the units and direction of change.

Since

0.75

is positive, the energy increases by

0.75

kWh for every additional

1

minute of charging time.

To formulate the final contextual interpretation of the slope.

Key Concept

Interpreting the slope of a linear equation in a real-world context

Question

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Step-by-Step Solution

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