Question

For each minute, the amount of water in the tank increases at a constant rate. So, we can draw a line through these two points to show the linear relationship between the number of minutes and the amount of water in the tank. Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line?
x
y
(3, 90)(6, 150)
0
1
2
3
4
5
6
7
8
9
10
0
15
30
45
60
75
90
105
120
135
150
165
180
195
210
Time (minutes)
Amount of Water (liters)
y= mx + b

Slope =

Answer 1

To find the slope \( m \) of the line that represents the relationship between time (in minutes) and the amount of water (in liters), we can use the two points provided: \((3, 90)\) and \((6, 150)\).

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in our points:
- \( (x_1, y_1) = (3, 90) \)
- \( (x_2, y_2) = (6, 150) \)

Now we can calculate the slope:

\[
m = \frac{150 - 90}{6 - 3} = \frac{60}{3} = 20
\]

So, the slope \( m \) is **20** liters per minute.

Now we can write the equation of the line in the form \( y = mx + b \) using this slope. To find \( b \), we can use one of the points, say \((3, 90)\):

Plugging \( x = 3 \) and \( y = 90 \) into the equation \( y = mx + b \):

\[
90 = 20(3) + b
\]
\[
90 = 60 + b
\]
\[
b = 90 - 60 = 30
\]

Thus, the equation of the line is:

\[
y = 20x + 30
\]

To summarize:
- The slope \( m \) is **20**.
- The equation of the line is \( y = 20x + 30 \).