This graph represents the linear relationship between the time in minutes and the gallons of gas in the boat. For each minute, the gallons of gas increases at a constant rate. What do the points (4, 50) and (10, 80) represent?
x
y
(4, 50)(10, 80)
0
2
4
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20
0
10
20
30
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50
60
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80
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130
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150
Time (minutes)
Gallons of gas
The point (4, 50) means that after
minutes, there are
gallons of gas in the boat.
The point (10, 80) means that after
minutes, there are
gallons of gas in the boat.
Great job!
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, 50)(10, 80)
0
2
4
6
8
10
12
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16
18
20
0
10
20
30
40
50
60
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80
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100
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130
140
150
Time (minutes)
Gallons of gas
y= mx + b
Slope =
Excellent!
Substitute the slope for m in our equation, or the rate of change of the gallons of gas.
x
y
(4, 50)(10, 80)
0
2
4
6
8
10
12
14
16
18
20
0
10
20
30
40
50
60
70
80
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100
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120
130
140
150
Time (minutes)
Gallons of gas
y= mx + b
y=
x+b
Slope = 5
Great job!
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, 50)(10, 80)
0
2
4
6
8
10
12
14
16
18
20
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
Time (minutes)
Gallons of gas
y=5x + b
b=
Excellent!
Let’s finish writing our equation to represent the relationship between time and the gallons of gas in the boat. Now that we know the amount of gas in the boat when Leo started filling it, b, substitute the vertical intercept for b in our equation.
x
y
(4, 50)(10, 80)
0
2
4
6
8
10
12
14
16
18
20
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
Time (minutes)
Gallons of gas
y
=
5x + b
y
=
5x +
b
=
30
Good work!
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 boat. How many gallons of gas will be in the boat after 20 minutes? Start by substituting 20 minutes for x in the equation.
y
=
5x
+
30
y
=
5
·
+
30
Good work!
Now, solve for y, the gallons of gas in the boat after 20 minutes.
y
=
5x
+
30
y
=
5·20
+
30
y
=
1 answer
To solve for \( y \) (the gallons of gas in the boat after 20 minutes), we'll use the equation you've provided:
\[ y = 5x + 30 \]
Now, substitute \( x = 20 \):
\[ y = 5(20) + 30 \]
Calculating that gives:
\[ y = 100 + 30 = 130 \]
So, after 20 minutes, there will be 130 gallons of gas in the boat.
