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 + 1.2 )

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have the same slope. The first equation is \( d = 2.5t + 2.2 \), so the slope (\( m \)) is \( 2.5 \). The second line must also have a slope of \( 2.5 \).

Step2: Use point - slope form (or slope - intercept form)

The slope - intercept form of a line is \( y=mx + b \) (here \( d=mt + b \)). We know the line passes through \( (t = 0,d = 1) \), which is the y - intercept (\( b \)) point. When \( t = 0 \), \( d=b \). So \( b = 1 \) and \( m = 2.5 \). So the equation is \( d=2.5t + 1 \).

Answer:

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