A hiker begins a climb at an elevation of 1,200 feet above sea level and climbs at a const… — SAT

A hiker begins a climb at an elevation of $1,200$ feet above sea level and climbs at a constant rate of $350$ feet per hour. The hiker's elevation, $E$ , in feet, $t$ hours after beginning the climb is given by the equation $E = 350t + 1,200$ . Which of the following is the best interpretation of $350$ in this context?

A
The starting elevation, in feet, of the hiker
The increase in the hiker's elevation, in feet, for each hour of climbingAnswer
C
The number of hours it takes the hiker to climb one foot
D
The total elevation, in feet, of the hiker after 350 hours of climbing

Answer

The increase in the hiker's elevation, in feet, for each hour of climbing

The coefficient of

t

, which is

350

, represents the rate of change of the hiker's elevation with respect to time. Since elevation is measured in feet and time is measured in hours, this rate is

350

feet per hour. Therefore, the value

350

represents the increase in the hiker's elevation, in feet, for each hour of climbing.

Step-by-Step Solution

Identify the structure of the linear equation.

The equation

E = 350t + 1,200

is in the slope-intercept form

y = mx + b

, where

m = 350

is the slope and

b = 1,200

is the

y

-intercept.

Linear equations in context have constant rates of change (slope) and starting values (

y

-intercept).

Determine the meaning of the slope in context.

The slope

350

represents the change in the dependent variable

E

(elevation in feet) per unit change in the independent variable

t

(time in hours).

The unit of the slope is the unit of the dependent variable divided by the unit of the independent variable, which is feet per hour.

Interpret the positive sign of the slope.

Since

350

is positive, the elevation increases by

350

feet for each hour of climbing.

A positive slope indicates a constant increase over time.

Key Concept

Interpreting slope in a linear context

Question

Answer

Step-by-Step Solution

Key Concept

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