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?
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What do you know about the slopes of parallel lines?
not very much i was out of school for a while in the hospital and i have to get this stuff dont to play football
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Slope is the tilt of a line.
If lines are parallel, they have the same slope.
In the equation
d = 2.5t + 2.2,
the 2.5 is the slope.
Since the other path is parallel, it must have the same slope, 2.5.
The other path must have an equation
d = 2.5t + b
where b is a number we will find.
We are given a point of the second path, (0, 1)
We replace t and d of the equation with t = 0 and with d = 1.
d = 2.5t + b, and we solve for b.
1 = 2.5(0) + b
1 = 0 + b
1 = b
We see that b = 1
Now we rewrite the equation of the second path using b = 1.
d = 2.5t + 1
That is the answer.