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Fabio is driving west away from Albany and towards Buffalo along Interstate 90 at a constant rate of speed
of 62 miles per hour. After driving for 1.5 hours, Fabio is 221 miles from Albany.

Fabio is driving west away from Albany and towards Buffalo along Interstate 90 at a constant rate of speed of 62 miles per hour After driving for 15 hours Fabi class=

Respuesta :

Answer:

a) ( D - 128 ) = m ( 1,5 - 0)

b) D = 62*h + 128

Step-by-step explanation:

Fabio drives at a constant speed of 62 miles per hour therefore:

62 * 1,5 = 93 miles

But he is 221 miles away from Albany, then he started

221 - 93 = 128 miles from Albany

In a coordinates system D (distance in the  y-axis ), and h ( hours in x-axis), we have two points

h₁ = 0 (h)  D (y intercept) = 128   miles       and   h = 1,5 (h)   D = 221 miles

P₁ ( 0 , 128 )      P₂ ( 1,5  , 221 )

Then the equation for straight-line passing through two points is:

m  = ( D - D₁ ) / ( h - h₁ )

( D - D₁ ) = m ( h - h₁ )

a) ( D - 128 ) = m ( 1,5 - 0)  

And

b)  m = 93/  1,5

m = 62

And  

b) D = mh + b

D = mh  + D₁

D = 62*h + 128

a)

The equation is:

[tex]D - 221 = 62(h - 1.5)[/tex]

b) Initially, he was 128 miles away from Albany.

Item a:

Fabio is traveling from Albany to Buffalo, and his distance D from Albany after h hours is modeled by a linear function in the following format:

[tex]D - D_1 = m(h - h_1)[/tex]

We have that:

  • Velocity of 62 miles per hour, thus the slope is [tex]m = 62[/tex].
  • After 1.5 hours, he is 221 miles away from Albany, thus the point is [tex]h_1 = 1.5, D_1 = 221[/tex].

The equation is:

[tex]D - D_1 = m(h - h_1)[/tex]

[tex]D - 221 = 62(h - 1.5)[/tex]

Item b:

  • The initial distance is D when h = 0, so:

[tex]D - 221 = 62(0 - 1.5)[/tex]

[tex]D = -1.5(62) + 221[/tex]

[tex]D = 128[/tex]

Initially, he was 128 miles away from Albany.

A similar problem is given at https://brainly.com/question/16302622

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