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The table shows the distance a runner covers during a race:

Time, x

(minutes)


Distance, y

(miles)
5 0.5
10 1
15 1.5
20 2
25 2.5
Which equation represents the relationship between x and y?

a. y = 0.5x
b. y = 10x
c. y = x + 10
d. y = 110x

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Answer :

Answer:

b. y=10x

Step-by-step explanation:

  • here, x represents time(minutes) : 0.5

                                                             1

                                                            1.5

                                                             2

                                                            2.5

y represents distance (miles): 5

                                                 10

                                                 15

                                                 20

                                                 25

  • to write any equation(linear) basically we need 2 points lying on it

let the 2 points be:  (1,10) and (2,20) [from the given information]

  • now, let (A,B) and (C,D) are two points on a line

then the equation of it can be given as :

[tex]y-B=(\frac{D-B}{C-A} )*(x-A)[/tex]

  • so, here the required equation will be,

[tex]y-10=(\frac{20-10}{2-1} )*(x-1)\\[/tex]

this is also equal to, [tex]y-10=10*(x-1)\\y-10=10x-10\\y     =10x-10+10\\y=10x[/tex]

  • therefore, option c represents the relationship between x and y.
  • [trick: when you have options, you can directly substitute x and respective y values and check if the equation satisfies it. the equation which satisfies all the x and respective y values will be the correct equation.]

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