Question

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
1
2
3
4
5
6
7
8
9
10
0
20
40
60
80
100
120
140
160
180
200
Time (minutes)
Amount of Water (liters)
y= mx + b
y=
x+b

Slope = 5

Answer 1

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.