Question

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

Answer 1

The correct option is:   A.  $d= 2.5t+1$

Explanation

The equation describing the graph of the position of the first object with respect to time is:  $d = 2.5t + 2.2$

If we compare the above equation with the standard slope-intercept form$(y=mx+b)$, then the slope of the above equation will be 2.5

As the slopes of the parallel lines are equal to each other, so the slope of the parallel line will be also 2.5

So, the equation of the parallel line will be:  $d= 2.5t+b$ , where $b$ is the y-intercept.

The parallel line is passing through (t = 0, d = 1). So, plugging these values into the above equation, we will get.....

$1=2.5(0)+b\\ \\ b=1$

So, the equation of the second graph will be:  $d= 2.5t+1$