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.

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

GPT-4o mini · 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.