Sam drives his car at a constant speed. he travels a distance (d) of 15 miles with 1 /2 of a gallon of gas (g). write an equation in the form of d=rg that represents the relationship between distance (d) and the number of gallons of gas (g), where r is the constant of proportionality. 

Hey there,

So we have to right an equation d=rg right?
So when d is the distance right?
And we know that the distance is 15.

So now we have 15=rg OK?

And g is the number of gallons of gas right? And he used half a gallon of gas.
So we have 15=r(1/2) right?

Now the thing is we don’t like fractions in equations so we have to get rid of it.
How can we change 1/2 into a whole number?
If we multiply by two we can get 1 right?
So we multiply by two.
When we multiply one side by two we also have to multiply the other side by two too to balance to equation out right?
So we have d(15)=r((1/2)2) right?
So we get 30=2r OK?

Now we are told we have to find r right?
If 30=2r r must be 15 right?
Because 30/2 is 15.

So we know that r is 15 now.
So we have the equation d=15g

Hope this helps