Question

Write and graph an equation in two variables that shows the relationship between time and the distance traveled. Rises 4 feet in 9 seconds.

Answer 1

Let the distance x, and the time t

So, x = mt + c

Where m is the slope or rate of change and c is constant

Suppose the particle start traveling from the rest at t = 0

So, c = 0

∴ x = mt

Rises 4 feet in 9 seconds.

so, rate of change = distance per time = x/t = (4/9) (feet/seconds)

∴ m = 4/9

∴ x = (4/9) t

So, the relationship between time and the distance traveled

⇒ x = (4/9) t

See the attached figure which represents the graph of the equation.