A student is running a 5-kilometer race. He runs 1 kilometer every 3 minutes. Select the function that describes his distance from the finish line. A) f(x) = - 1 over 3 x + 5 B) f(x) = - 1 over 5 x + 3 C) f(x) = 1 over 5 x + 5 D) f(x) = 1 over 3 x + 3

The function that describes his distance from the finish line is f(x) = - 1/3 x + 5. The correct answer between all the choices given is the first choice or letter A. I am hoping that this answer has satisfied your query about this specific question.

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InesWalston InesWalston · Answer 2 · 2018-12-03T12:27:59+01:00

Answer:

[tex]\boxed{\boxed{y=5-\dfrac{1}{3}x}}[/tex]

Step-by-step explanation:

A student is running a 5-kilometer race i.e the total distance is 5 km.

He runs 1 kilometer every 3 minutes.

So the speed will be,

[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{time}}[/tex]

[tex]\text{Speed}=\dfrac{1}{3}[/tex]

Speed is the rate of change or slope and as the total distance is decreasing with time so it will in negative, hence

[tex]\text{Slope}=-\dfrac{1}{3}[/tex]

So when on x axis time and y axis distance is represented, 5 will be the y intercept.

Then putting all the values in slope intercept form of straight line,

[tex]\Rightarrow y=mx+c[/tex]

[tex]\Rightarrow y=-\dfrac{1}{3}x+5[/tex]

[tex]\Rightarrow y=5-\dfrac{1}{3}x[/tex]