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?

Answer 1

the relationship between d and t is linear, so it can be modelled as a linear y = mx + b equation (plugging in d and t as appropriate, you can think of it as d = mt + b instead). comparing it to the first equation d = 2.5t + 2.2, can you determine what your m-value would be?

now, once you have your m-value, let's look at the second object as a parallel passing through (t = 0, d = 1). because the second graph is parallel, it will have the same m-value as you determined from the first step. finally, you can plug your t, d, and m values into d = mt + b to solve for the constant b.

finally, you can re-write d = mt + b, plugging in just the m and b you solved for to get the equation.