Question

Graph the line that represents a proportional relationship between ddd and ttt with the property that an increase of 555 units in ttt corresponds to an increase of 888 units in ddd. What is the unit rate of change of ddd with respect to ttt? (That is, a change of 111 unit in ttt will correspond to a change of how many units in ddd?) The unit rate is .

Answer 1

a) The unit rate of change of d with respect to t is equal to 1.6

b) the graph of the line in the attached figure.

Step-to-step explanation:

we know that

A relationship between two variables t and d represent a proportional variation if it can be expressed in a form of d/t = k

or d = kt

step 1:- find the value of k

we have

t = 5 , d = 8

k = d/t

k = 8/5

k = 1.6

so, the linear equation is equal to d = 1.6t

step 2 :- using a graphing tool

graph the line d = 1.6t

Answer 2

Given: A proportional relationship between d  and t  with the property that an increase of 5 units in t  corresponds to an increase of 8  units in d .

To Find : Unit rate of change of d  with respect to t  

Graph the line

Solution:

an increase of 5 units in t  corresponds to an increase of 8  units in d

=> Slope  =   Δd/Δt   = 8/5 = 1.6

proportional relationship between d  and t

=> d ∝ t

=> d = 1.6t

t           d=1.6t

0          0

1           1.6

2           3.2

3           4.8

Plot the points and draw a line passing through points

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