Answer:
Part 5)
a) [tex]y=\frac{1}{16}x[/tex]
b) [tex]y=9.5\ pounds[/tex]
Part 6)
a) [tex]y=50x[/tex]
b) [tex]y=700\ pencils[/tex]
Step-by-step explanation:
The complete questions in the attached figure
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
Part 5) The number of pounds in a bag of flour varies directly with the number of ounces. Write a direct variation equation that describes the relationship. Use your equation to determine the number of pounds in 152 ounces.
Part a) Write a direct variation equation that describes the relationship
Let
x ------> number of ounces
y ----> number of pounds
Observing the graph we have
The point (16,1)
so
[tex]x=16\ ounces[/tex]
[tex]y=1\ pounds[/tex]
Fin the value of the constant of proportionality k
[tex]k=y/x[/tex]
substitute the values
[tex]k=\frac{1}{16}\frac{pounds}{ounce}[/tex]
The equation of the direct variation is
[tex]y=\frac{1}{16}x[/tex]
Part b) Use your equation to determine the number of pounds in 152 ounces
we have
[tex]y=\frac{1}{16}x[/tex]
For [tex]x=152\ ounces[/tex]
substitute the value of x in the equation and solve for y
[tex]y=\frac{1}{16}(152)[/tex]
[tex]y=9.5\ pounds[/tex]
Part 6) The number of pencils for sale varies directly with the number of boxes. Write a direct variation equation that describes the relationship. Use your equation to determine the number of pencils in 14 boxes.
Part a) Write a direct variation equation that describes the relationship
Let
x ------> number of boxes
y ----> number of pencils
Observing the graph we have
The point (1,50)
so
[tex]x=1\ box[/tex]
[tex]y=50\ pencils[/tex]
Fin the value of the constant of proportionality k
[tex]k=y/x[/tex]
substitute the values
[tex]k=\frac{50}{1}=50\frac{pencils}{box}[/tex]
The equation of the direct variation is
[tex]y=50x[/tex]
Part b) Use your equation to determine the number of pencils in 14 boxes.
we have
[tex]y=50x[/tex]
For [tex]x=14\ boxes[/tex]
substitute the value of x in the equation and solve for y
[tex]y=50(14)[/tex]
[tex]y=700\ pencils[/tex]
