Question

Phil is riding his bike. He rides 46 miles in 4 hours, 57.5 miles in 5 hours, and 69 miles in 6 hours. Find the constant of proportionality and write an equation to describe the situation. Let x represent the number of hours.

Answer 1

The constant of proportionality k = 11.5.

The equation will be:
`\mathbf{y=11.5(x)}`

Explanation:

If x represents number of hours than y represents miles

We are given:

x y

4 46

5 57.5

6 69

The constant of proportionality can be found using formula:
`k=(y)/(x)`

Putting values and finding k

x y k (
`k=(y)/(x)`)

4 46 11.5

5 57.5 11.5

6 69 11.5

So, the constant of proportionality k = 11.5

Now, The equation will be:

`k=(y)/(x)\\or \\y=kx\\Put \ k=11.5\\y=11.5(x)`

So, the equation will be:
`\mathbf{y=11.5(x)}`