Answer:
Part 1) The unit rate is [tex]16\frac{dollars}{ounce}[/tex]
Part 2) The unit rate is [tex]\frac{1}{4}\frac{dollars}{ounce}[/tex]
Part 3) The unit rate is [tex]\frac{1}{4}\frac{dollars}{ounce}[/tex]
Part 4) The unit rate is [tex]4\frac{dollars}{ounce}[/tex]
see the attached figure
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{d2-d1}{n2-n1}[/tex]
where
d ----> number of dollars (dependent variable or output value)
n ---> number of ounces (independent variable or input value)
Remember that the slope of the linear equation is the same that the unit rate
Verify each case
1) we have
[tex]d=16n[/tex]
This is a proportional relationship between the variables d and n
The slope is
[tex]m=16\frac{dollars}{ounce}[/tex]
therefore
The unit rate is [tex]16\frac{dollars}{ounce}[/tex]
2) we have
First table
take two points from the table
(4,1) and (16,4)
substitute in the formula of slope
[tex]m=\frac{d2-d1}{n2-n1}[/tex]
[tex]m=\frac{4-1}{16-4}[/tex]
[tex]m=\frac{3}{12}\frac{dollars}{ounce}[/tex]
simplify
[tex]m=\frac{1}{4}\frac{dollars}{ounce}[/tex]
therefore
The unit rate is [tex]\frac{1}{4}\frac{dollars}{ounce}[/tex]
3) we have
[tex]n=4d[/tex]
This is a proportional relationship between the variables d and n
isolate the variable d
[tex]d=\frac{1}{4}n[/tex]
The slope is
[tex]m=\frac{1}{4}\frac{dollars}{ounce}[/tex]
therefore
The unit rate is [tex]\frac{1}{4}\frac{dollars}{ounce}[/tex]
4) we have
Second table
take two points from the table
(1,4) and (2,8)
substitute in the formula of slope
[tex]m=\frac{d2-d1}{n2-n1}[/tex]
[tex]m=\frac{8-4}{2-1}[/tex]
[tex]m=4\frac{dollars}{ounce}[/tex]
therefore
The unit rate is [tex]4\frac{dollars}{ounce}[/tex]
