Sammy fills her bus with gas. The bus has some gas in it, and Sammy fills it at a constant rate each minute. Write an equation that represents this situation. Then use the equation to make a prediction.

Question

Sammy fills her bus with gas. The bus has some gas in it, and Sammy fills it at a constant rate each minute. Write an equation that represents this situation. Then use the equation to make a prediction.
This graph represents the linear relationship between the time in minutes and the gallons of gas in the bus. For each minute, the gallons of gas increases at a constant rate. What do the points (4, 75) and (14, 175) represent?
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
The point (4, 75) means that after 
 minutes, there are 
 gallons of gas in the bus.

The point (14, 175) means that after 
 minutes, there are 
 gallons of gas in the bus.
Good work!
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? In other words, what is the change in gallons of gas for each minute?
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
y= mx + b

Slope = 
Great job!
Substitute the slope for m in our equation, or the rate of change of the gallons of gas.
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
y= mx + b
y= 
 x+b

Slope = 10
Excellent!
Now, solve for b, or the vertical intercept. You can can substitute the x and y-values for a point on the line into the equation to help you. Solve on paper or use the calculator. Then, enter your answer on Zearn.
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
y=10x + b

b= 
Excellent!
Let’s finish writing our equation to represent the relationship between time and the gallons of gas in the bus. Now that we know the amount of gas in the bus when Sammy started filling it, b, substitute the vertical intercept for b in our equation.
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
y
=
10x + b
y
=
10x + 
b
=
35
Nice!
Let’s use the equation to help us make a prediction. Remember x represents the time in minutes, and y represents the gallons of gas in the bus. How many gallons of gas will be in the bus after 18 minutes? Start by substituting 18 minutes for x in the equation.
y
=
10x
+
35
y
=
10
·
+
35
You got it!
Now, solve for y, the gallons of gas in the bus after 18 minutes.
y
=
10x
+
35
y
=
10·18
+
35
y
=

GPT-4o mini · Answer

To solve for $ y $ (the gallons of gas in the bus after 18 minutes), we will substitute $ x = 18 $ into the equation $ y = 10x + 35 $. Starting with the equation: $$ y = 10 \cdot 18 + 35 $$ Now, calculate $ 10 \cdot 18 $: $$ 10 \cdot 18 = 180 $$ Now, add $ 35 $: $$ y = 180 + 35 = 215 $$ Thus, the number of gallons of gas in the bus after 18 minutes will be: $$ \boxed{215} $$ ### Summary of Key Points - **Points (4, 75) and (14, 175)** represent the following: - (4, 75): After 4 minutes, there are 75 gallons of gas in the bus. - (14, 175): After 14 minutes, there are 175 gallons of gas in the bus. - The equation representing the relationship between time and gallons of gas is: $$ y = 10x + 35 $$ Where: - $ m $ (the slope) is 10 (gallons of gas per minute). - $ b $ (the y-intercept) is 35 (the initial amount of gas in the bus).