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Find the constant of proportionality and unit rate for the data in the table. Then write the equation to represent the relationship between time t and distance d
Time Distance
2 hrs 90 miles
3 hrs 135 miles
5 hrs 225 miles
6 hrs 270 miles
I need step by step... Please.

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olemakpadu

Time          Distance                Distance / Time

2hrs          90 miles                  90 miles / 2 hrs =  45 miles / hr

3hrs          135 miles                135 miles / 3 hrs =  45 miles / hr

5hrs          225 miles                 225 miles / 5 hrs =  45 miles / hr

6hrs          270 miles                  270 miles / 6 hrs =  45 miles / hr


Constant of proportionality is 45 miles / hr. This is the same for the four values. The unit rate is also 45 miles / hr.


Let us assume the Distance , d is directly proportional to Time, t

d α t

d = kt

Constant of proportionality is k which is D/T

d = 45t
raphealnwobi

The constant of proportionality is 45 miles per hour

A linear equation is given by:

y = mx + b

where y, x are variables, m is the rate of change, b is the initial vale of y (y intercept).

Let d represent the distance and t represent the time.

Using the points (2, 90) and (6, 270):

[tex]d-d_1=\frac{d_2-d_1}{t_2-t_1}(t-t_1)\\\\d-90=\frac{270-90}{6-2}(t-2)\\\\d-90=45t-90\\\\d=45t[/tex]

Therefore the constant of proportionality is 45 miles per hour

Find out more at: https://brainly.com/question/13911928

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