Answer:
Explanation:
To find the unit rate, just stack these two units and make it a fraction to simplify it to its furthest.
$15 per 5 gallons of gas
15/5 = 3/1
The unit rate is $3 per a gallon of gas.
Now, let's put this into an equation of y = kx, first let's figure out what y, k, and x means.
"K" represents the constant of proportionality, meaning how the other two variables are related to each other.
"Y" represents the dependent variable and "X" represents the independent variable. So y depends on x.
To put this into an equation, use the unit rate and plug it into "K".
Since we figured out the rate is 3, the equation would be:
y = 3x
The constant of proportionality is 3.
To fill in the table above, we use the unit rate to help us.
x - gallons: 0 1 2 3 4 5 6 7 8
__________________________
y - $ spent: 0 _ _ _ _ _ _ _ _
1 gallon would equal $3(1 · 3)-- is already given by the unit rate, so, the y-value would be 3 if x is 1.
2 gallons would equal $6(2 · 3), so the y-value would be 6 if x is 2.
3 gallons would equal $9(3 · 3), so the y-value would be 9 if x is 3.
4 gallons would equal $12(4 · 3), so the y-value would be 12 if x is 4.
5 gallons would equal $15(5 · 3), so the y-value would be 15 if x is 5.
6 gallons would equal $18(6 · 3), so the y-value would be 18 if x is 6.
7 gallons would equal $21(7 · 3), so the y-value would be 21 if x is 7.
8 gallons would equal $23(8 · 3), so the y-value would be 23 if x is 8.
You get the idea if you keep progressing with the x-values, just keep multiplying x by the unit rate/constant of proportionality to get the y-values.
Our new table would be:
x - gallons: 0 1 2 3 4 5 6 7 8
___________________________
y - $ spent: 0 3 6 9 12 15 18 21 24