You are adding orange juice to a 10-liter capacity jar. The equation 3x - 2y = -5 relates the amount of juice y, in liters, with the number of minutes, x, you add juice. How much juice was in the jar to start? At what rate is the jar filled?
Answers
Answer: 5/2 liters (or 2.5 liters) of juice were in the jar to start.
The jar was filled at a rate of 5 minutes.
Step-by-step explanation:
Firstly, rearrange the equation so that y = mx + b. If you move the x over, you get -2y = -3x -5. To get rid of the -2 in front of the y, divide both sides by -2. Then you get y = 3/2x + 5/2.
The amount of juice in the jar initially is b, also known as the y-intercept.
If you look at the equation, you see that 5/2 is our y-intercept which means the jar initially had 5/2 liters of juice at the start (this is the same as 2.5 liters because 5 divided by 2 is 2.5).
To find the rate at which the jar was filled, you need to solve for x. Plug in the 10 liters for the y and solve.
y = 3/2x + 5/2
10 = 3/2x + 5/2
Now, subtract 5/2 from both sides.
7.5 = 3/2x
Divided both sides by 3/2 to get x alone, which will give you the number of minutes in which the jar was filled. 5 = x
The jar was filled at a rate of 5 minutes.
Answer:
Firstly, rearrange the equation so that y = mx + b. If you move the x over, you get -2y = -3x -5.
To get rid of the -2 in front of the y, divide both sides by -2. Then you get y = 3/2x + 5/2.
The amount of juice in the jar initially is b,
also known as the y-intercept.
If you look at the equation, you see that 5/2 is our y-intercept which means the jar initially had 5/2 liters of juice at the start (this is the same as 2.5 liters because 5 divided by 2 is 2.5).
To find the rate at which the jar was filled, you need to solve for x. Plug in the 10 liters for the y and solve.
y = 3/2x + 5/2
10 = 3/2x + 5/2
Now, subtract 5/2 from both sides.
7.5 = 3/2x
Divided both sides by 3/2 to get x alone, which will give you the number of minutes in which the jar was filled.
5 = x