To represent the relationship between time and the amount of water in the tank, a linear equation can be written in the form y=mx+b. In this equation, m is the slope of the line, or the rate of change of water in the tank. We just solved for and interpreted the slope. Substitute the slope for m in our equation.

x
y
(3, 100)(7, 120)
0
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5
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0
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Time (minutes)
Amount of Water (liters)
y= mx + b
y=
x+b

Slope = 5

1 answer

Given the slope \( m = 5 \), we can substitute that into the linear equation format \( y = mx + b \). This gives us:

\[ y = 5x + b \]

Next, we need to determine the value of \( b \), which represents the y-intercept (the amount of water in the tank when \( x = 0 \)).

To find \( b \), we can use one of the given points from the table: either \( (3, 100) \) or \( (7, 120) \). We'll use the point \( (3, 100) \).

Substituting \( x = 3 \) and \( y = 100 \) into the equation:

\[ 100 = 5(3) + b \]

Calculating \( 5(3) \):

\[ 100 = 15 + b \]

Now, isolating \( b \):

\[ b = 100 - 15 \] \[ b = 85 \]

Now that we have both \( m \) and \( b \), we can rewrite the equation:

\[ y = 5x + 85 \]

This equation represents the relationship between the time (\( x \), in minutes) and the amount of water (\( y \), in liters) in the tank.