Question

select the correct answer.
two objects are moving along separate linear paths where each path is described by position, d, and time, t. the variable d is measured in meters, and the variable t is measured in seconds. the equation describing the graph of the position of the first object with respect to time is ( d = 2.5t + 2.2 ). the graph of the position of the second object is a parallel line passing through ( (t = 0, d = 1) ). what is the equation of the second graph?
a. ( d = 2.5t + 1 )
b. ( d = t + 2.5 )
c. ( d = -0.4t + 1 )
d. ( d = 2.5t + 3.2 )

Explanation:

Step1: Recall parallel line equation property

Parallel lines have the same slope. The first object's equation is \( d = 2.5t + 2.2 \), so the slope (coefficient of \( t \)) is \( 2.5 \). Thus, the second object's equation must also have a slope of \( 2.5 \).

Step2: Use the point \((t = 0, d = 1)\)

The general form of a linear equation is \( d = mt + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know \( m = 2.5 \), and when \( t = 0 \), \( d = 1 \). Substituting \( t = 0 \), \( d = 1 \), and \( m = 2.5 \) into \( d = mt + b \):

$$ 1=2.5\times0 + b $$

So, \( b = 1 \).

Step3: Write the equation

Substituting \( m = 2.5 \) and \( b = 1 \) into \( d = mt + b \), we get \( d = 2.5t+1 \).

Answer:

A. \( d = 2.5t + 1 \)