Phil is riding his bike. He rides 23 miles in 2 hours, 34.5 miles in 3 hours, and 46 miles in 4 hours. Find the constant of proportionality and write an equation to describe the situation. Let x represent the number of
hours.
The constant of proportionality is k =
The equation that describes the relationship is y =

Constant = 11.5

y = 11.5x.

Step-by-step explanation:

This is direct variation so the equation of proportionality is

y = kx where y = miles, x = hours and  k is a constant.

23 =  2k

k = 11.5

34.5 = 3k

k = 11.5

46 = 4k

k = 11.5

The equation is my= 11.5x.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.