Answer: Option B
[tex]y=0.5x +0.75[/tex]
Step-by-step explanation:
The equation modeling this situation is a linear equation of the form
[tex]y = mx + b[/tex]
Where x is the slope and b is the intercept with the y axis.
To find the equation of a line we need two points that belong to the line.
We know that when it is empty the jug weighs 0.75 lib.
This is:
When x = 0, y = 0.75
Then when the jug contains 3 cups of water it weighs 2.25 pounds.
This is:
When x = 3, y = 2.25
We already have the two points
Then we find the slope of the straight
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_2 = 2.25\\\\y_1=0.75\\\\x_2=3\\\\x_1=0[/tex]
[tex]m=\frac{2.25-0.75}{3-0}[/tex]
[tex]m = 0.5[/tex]
The equation is:
[tex]y=0.5x +b[/tex]
We substitute the point (0, 0.75) in the equation and solve for b
[tex]0.75=0.5(0) +b[/tex]
[tex]b=0.75[/tex]
Finally the equation is:
[tex]y=0.5x +0.75[/tex]
